# What describes the sequence 1 1 2 3 5 is it arithmetic or geometric?

It is an arithmetic sequence. To differentiate arithmetic from geometric sequences, take any three numbers within the sequence. If the middle number is the average of the two on either side then it is an arithmetic sequence. If the middle number squared is the product of the two on either side then it is a geometric sequence.

The sequence 0, 1, 1, 2, 3, 5, 8 and so on is the Fibonacci series, which is an arithmetic sequence, where the next number in the series is the sum of the previous two numbers. Thus F(n) = F(n-1) + F(n-2). Note that the Fibonacci sequence always begins with the two numbers 0 and 1, never 1 and 1.

### Can a sequence of numbers be both geometric and arithmetic?

Yes, it can both arithmetic and geometric. The formula for an arithmetic sequence is: a(n)=a(1)+d(n-1) The formula for a geometric sequence is: a(n)=a(1)*r^(n-1) Now, when d is zero and r is one, a sequence is both geometric and arithmetic. This is because it becomes a(n)=a(1)1 =a(1). Note that a(n) is often written an It can easily observed that this makes the sequence a constant. Example: a(1)=a(2)=(i) for i= 3,4,5... if a(1)=3 then for a geometric… Read More

### Can a recursive formula produce an arithmetic or geometric sequence?

arithmetic sequence * * * * * A recursive formula can produce arithmetic, geometric or other sequences. For example, for n = 1, 2, 3, ...: u0 = 2, un = un-1 + 5 is an arithmetic sequence. u0 = 2, un = un-1 * 5 is a geometric sequence. u0 = 0, un = un-1 + n is the sequence of triangular numbers. u0 = 0, un = un-1 + n(n+1)/2 is the sequence… Read More

### Is constant sequence an AP?

It is an arithmetic sequence (with constant difference 0), or a geometric sequence (with constant ratio 1).

### What is the difference between a geometric sequence and arithmetic sequence?

Goemetric sequence : A sequence is a goemetric sequence if an/an-1is the same non-zero number for all natural numbers greater than 1. Arithmetic sequence : A sequence {an} is an arithmetic sequence if an-an-1 is the same number for all natural numbers greater than 1.

### What is the difference between an arithmetic series and a geometric series?

An arithmetic series is the sequence of partial sums of an arithmetic sequence. That is, if A = {a, a+d, a+2d, ..., a+(n-1)d, ... } then the terms of the arithmetic series, S(n), are the sums of the first n terms and S(n) = n/2*[2a + (n-1)d]. Arithmetic series can never converge. A geometric series is the sequence of partial sums of a geometric sequence. That is, if G = {a, ar, ar^2, ..., ar^(n-1)… Read More

### What is the Relation between geometric mean and arithmetic mean?

The mean of the numbers a1, a2, a3, ..., an is equal to (a1 + a2 + a3 +... + an)/n. This number is also called the average or the arithmetic mean. The geometric mean of the positive numbers a1, a2, a3, ... an is the n-th roots of [(a1)(a2)(a3)...(an)] Given two positive numbers a and b, suppose that a< b. The arithmetic mean, m, is then equal to (1/2)(a + b), and, a, m… Read More

### How do you find the nth number in a sequence?

tn = t1+(n-1)d -- for arithmetic tn = t1rn-1 -- for geometric

### What does geometric sequence?

You mean what IS a geometric sequence? It's when the ratio of the terms is constant, meaning: 1, 2, 4, 8, 16... The ratio of one term to the term directly following it is always 1:2, or .5. So like, instead of an arithmetic sequence, where you're adding a specific amount each time, in a geometric sequence, you're multiplying by that term.

### What are the numbers whose sum is 3 form an arithmetic sequence and their squares form geometric sequence?

The numbers are: 1-sqrt(2), 1 and 1+sqrt(2) or approximately -0.414214, 1 and 2.414214

### Is the sequence 2 3 5 8 12 arithmetic or geometric?

It is neither. It is a quadratic sequence. Un = (x2 - x + 4)/2 for n = 1, 2, 3, ...

### What is a geometric property?

1.The Geometric mean is less then the arithmetic mean. GEOMETRIC MEAN < ARITHMETIC MEAN 2.

### Is 1 1 1 1 1 an arithmetic sequence?

Yes, with a difference of zero between terms. It is also a geometric series, with a ratio of 1 in each case.

### What is the formula for sequence sum?

There are different answers depending upon whether the sequence is an arithmetic progression, a geometric progression, or some other sequence. For example, the sequence 4/1 - 4/3 + 4/5 - 4/7 adds to pi

### How do you find out the nth term?

by the general formula ,a+(n-1)*d * * * * * That assumes that it is an arithmetic sequence. The sequence cound by geometric ( t(n) = a*rn ) or power ( t(n) = n2 ) or something else.

### Properties and limitations of geometric mean?

In a given sequence, there are two possible means calculatable: Arithmetic Mean, and Geometric Mean. The arithmetic mean, as we all know, is calculated from the sum of all the numbers divided by how many numbers there are: Sumn/n. The Geometric sum is calculated by multiplying all the numbers within the sequence together and taking the nth root of this value: (Productn)(1/n). In a geometric series, N(i)= a(ri), the geometric mean is found to be… Read More

### Descending geometric sequence?

A descending geometric sequence is a sequence in which the ratio between successive terms is a positive constant which is less than 1.

### Rule to finding terms in a arithmetic sequence?

The nth term of an arithmetic sequence = a + [(n - 1) X d]

### Who was the founder of arithmetic sequence?

One of the simplest arithmetic arithmetic sequence is the counting numbers: 1, 2, 3, ... . The person who discovered that is prehistoric and, therefore, unknown.

### How many possible sequences of four numbers are there from 1 to 8?

Question is not very clear about the context of word 'sequence' here. If I am to select 4 numbers out of four and arrange them in order then there are 4!*8C4 = 1680 different sequences possible. If the word sequence refers to some arithmetic sequence or geometric sequence, then counting is going to change for sure.

### What number comes next in the sequence 0-1-2-4-16?

The differences are not the same so the sequence is not arithmetic. The sequence starts with a zero, so it cannot be geometric, or an exponential (power) sequence. The quartic: (2n4 - 19n3 + 64n2 - 83n + 36)/6 fits the 5 points. That gives the next term as 55.

### What is ascending geometric sequence?

A geometric sequence is : a•r^n which is ascending if a is greater than 0 and r is greater than 1.

### This is Q of sequence series hlp me1 2 4 8 16 ..find nth term of the series find sum of first n term?

If you remember taking sequences, you'll recall that there are three main types: 1)Arithmetic Sequence 2)Geometric Sequence 3)Varied-formula Sequence If the difference between the terms is additional or subractional then its an arithmetic sequence, lets check if this is the case, subtract the first term from the second and the second from the third etc : 1, 2, 4, 8, 16 2-1=1 4-2=2 8-4=4....all the answers are not constant so it is not an arithmetic… Read More

### What is mathematical sequence?

Sequences are a group of numbers that follow a certain pattern. There are two kinds of sequences, the arithematic sequence and geometric sequence. Arithematic sequence follows through addition (and subtraction). Geometric sequence follows throug multiplication (and division). Arithematic Sequence Example : 1, 6, 11, 16, 21 The pattern follows an addition of 5. Geometric Sequence Example : 1, 3, 9, 27, 81 The pattern follows a multiplication of 3

### Difference between AP series GPs reis?

AP - Arithmetic Progression GP - Geometric Progression AP: An AP series is an arithmetic progression, a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 3, 5, 7, 9, 11, 13, … is an arithmetic progression with common difference 2. If the initial term of an arithmetic progression is and the common difference of successive members is d, then the nth term of the sequence is… Read More

### Is the sequence 1361015 geometric?

Of sorts. 1 3 6 10 15 would have a geometric representation, but would not fit the definition of a "geometric sequence". One example of a geometric representation of the sequence would be the number of total bowling pins as you add each row. The first row as 1 pin, the second has 2, then 3,4,5. 1 = 1 + 2 = 3 + 3 = 6 + 4 = 10 + 5 = 15

### What is a good example of an arithmetic sequence?

An excellent example of an arithmetic sequence would be: 1, 5, 9, 13, 17, in which the numbers are going up by four, thus having a common difference of four. This fulfills the requirements of an arithmetic sequence - it must have a common difference between all numbers.

### Is the Fibonacci sequence a geometric sequence?

No. Although the ratios of the terms in the Fibonacci sequence do approach a constant, phi, in order for the Fibonacci sequence to be a geometric sequence the ratio of ALL of the terms has to be a constant, not just approaching one. A simple counterexample to show that this is not true is to notice that 1/1 is not equal to 2/1, nor is 3/2, 5/3, 8/5...

### How can you tell if a infinite geometric series has a sum or not?

The geometric series is, itself, a sum of a geometric progression. The sum of an infinite geometric sequence exists if the common ratio has an absolute value which is less than 1, and not if it is 1 or greater.

### Algebra words that start with g?

· Geometric Sequence (geometric progression) - a sequence of numbers in which each term is obtained by multiplying the preceding term by the same number (common ratio). The following is a geometric progression: 1, 2, 4, 8, 16, 32… The common ratio for this geometric progression is 2.

### What are arithmetic series?

An arithmetic series is a fairly similar to an arithmetic sequence except for the fact that in a series you are adding the numbers in between, not putting commas. Example: Sequence 1,3,5,7,.........n Series 1+3+5+7+..........+n Hope this helped(:

### What does Geometric Series represent?

A geometric series represents the partial sums of a geometric sequence. The nth term in a geometric series with first term a and common ratio r is:T(n) = a(1 - r^n)/(1 - r)

### What is the 19th term in the arithmetic sequence 11 7 3 -1?

This is the real question what is the 19th term in the arithmetic sequence 11,7,3,-1,...? _________________________________________________________ Looks like you just subtract 4 each time, as : 11,7,3,-1,-5,-9, ......

### What is every term of a sequence is 1?

It is a valid sequence which is fundamental to arithmetic since its partial sums define the counting numbers.

### The sum of the first 5 terms of an arithmetic sequence is 40 and the sum of its first ten terms is 155what is this arithmetic sequence?

a1=2 d=3 an=a1+(n-1)d i.e. 2,5,8,11,14,17....

### How do you use a arithmetic sequence to find the nth term?

The difference between successive terms in an arithmetic sequence is a constant. Denote this by r. Suppose the first term is a. Then the nth term, of the sequence is given by t(n) = (a-r) + n*r or a + (n-1)*r

### What is a real life sequence that demonstrates an arithmetic sequence?

Your age on January 1 each year. Or, the year number on January 1 each year.

### How do you find the common ratio in a geometric sequence?

Divide any term in the sequence by the previous term. That is the common ratio of a geometric series. If the series is defined in the form of a recurrence relationship, it is even simpler. For a geometric series with common ratio r, the recurrence relation is Un+1 = r*Un for n = 1, 2, 3, ...

### What is the formula to find the sum of a geometric sequence?

The formula to find the sum of a geometric sequence is adding a + ar + ar2 + ar3 + ar4. The sum, to n terms, is given byS(n) = a*(1 - r^n)/(1 - r) or, equivalently, a*(r^n - 1)/(r - 1)

### How do you find terms in arithmetic sequences?

The following formula generalizes this pattern and can be used to find ANY term in an arithmetic sequence. a'n = a'1+ (n-1)d.

### Is 2 6 18 54 an arithmetic sequence?

No it is not.U(2) - U(1) = 6 - 2 = 4 U(3) - U(2) = 18 - 6 = 12 Since 4 is different from 12, it is not an arithmetic sequence.

### How do you generate harmonic progression?

If a sequence A = {a1, a2, a3, ... } is an arithmetic progression then the sequence H = {1/a1, 1/a2, 1/a3, ... } is a harmonic progression.

### Is the Fibonacci sequence geometric?

No, but it can be expressed as the sum of two geometric sequences. F_n = a^n + b^n a = (1+sqrt{5})/2 b = (1-sqrt{5})/2

### What is the tenth number in the sequence 1 -17 -35 -53?

This is an arithmetic sequence with t1 = 1 and the common difference d = -18. The nth term of an arithmetic sequence is given by the formula: tn = t1 + (n - 1)d (substitute 10 for n, 1 for t1, and -18 for d) t10 = 1 + (10 - 1)(-18) = 1 + 9(-18) = 1 - 162 = -161 Thus the 10th number of the sequence is -161.

### What is the sum of the first 15 terms of an arithmetic?

For an Arithmetic Progression, Sum = 15[a + 7d].{a = first term and d = common difference} For a Geometric Progression, Sum = a[1-r^15]/(r-1).{r = common ratio }.

### What maths sequences can you start with 4 and 8?

one rule would be an+1 = an + 4 ; a0= 4. This gives 4,8,12,16,20,..... This is called an arithmetic sequence. A geometric rule would be an+1 = 2an; a0= 4. This gives 4,8,16,32,64,... Another rule is an+1 = an/2 + 6 ; a0= 4. This gives 4, 8, 10, 11, 11.5,11.75, ....

### What is descending geometric sequence?

A geometric sequence is a sequence where each term is a constant multiple of the preceding term. This constant multiplying factor is called the common ratio and may have any real value. If the common ratio is greater than 0 but less than 1 then this produces a descending geometric sequence. EXAMPLE : Consider the sequence : 12, 6, 3, 1.5, 0.75, 0.375,...... Each term is half the preceding term. The common ratio is therefore… Read More

### What is 2 8 32 128 in gemetric sequence?

Not sure what a gemetric sequence might be. 2 8 32 128 is the start of the geometric sequence defined by Un = 22n-1 for n = 1, 2, 3, ...

### What is the definition of an arithmetic sentence?

An arithmetic sequence is a sequence of numbers such that the difference between successive terms is a constant. This constant is called the common difference and is usually denoted by d. If the first term is a, then the iterative definition of the sequence is U(1) = a, and U(n+1) = U(n) + d for n = 1, 2, 3, ... Equivalently, the position-to-term rule which defines the sequence is U(n) = a + (n-1)*d… Read More