You need to know two numbers to completely describe the geometric sequence: the starting number, and the ratio between each number and the previous one.
When you use recursion, you always need a "base case", otherwise, the recursion will repeat without end.
In words, if "n" is 1, the result is the starting term. Otherwise, it is the ratio times the "n-1"th term.
The following version is appropriate for a programming language (written here in pseudocode, i.e., not for a specific language):
function geometric(starting_number, ratio, term)
if term = 1:
result = starting_number
else:
result = ratio * geometric(starting_number, ratio, term - 1)
In this case, 22 would have the value of 11.
In order to answer the question is is necessary to know what the explicit formula was. But, since you have not bothered to provide that information, the answer is .
2946
previous * 2 Since each term after the first is the product of the preceding term and 2 (a constant which can be found by dividing any term by its predecessor and is called the common ratio, r), this is a geometric sequence. In general, if the nth term of a geometric sequence is represented by an, then an = a1rn-1 In our case, a = 3 and r = 2, so the formula for the sequence becomes, an = 3 x 2n-1
1240
In this case, 22 would have the value of 11.
Yes, that's what a geometric sequence is about.
Recursive Form
In order to answer the question is is necessary to know what the explicit formula was. But, since you have not bothered to provide that information, the answer is .
2946
previous * 2 Since each term after the first is the product of the preceding term and 2 (a constant which can be found by dividing any term by its predecessor and is called the common ratio, r), this is a geometric sequence. In general, if the nth term of a geometric sequence is represented by an, then an = a1rn-1 In our case, a = 3 and r = 2, so the formula for the sequence becomes, an = 3 x 2n-1
Yes, it can.
A sequence usually has a position-to-value function. Alternatively, it can be derived from the recursive relationship that defines the sequence.
1240
A sequence is geometric if each term is found by mutiplying the previous term by a certain number (known as the common ratio). 2,4,8,16, --> here the common ratio is 2.
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.
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 10.