U1 = a = 21
U6 = ar5 = 352947
where Un is the nth term, with first term, a, and commn ratio r.
Dividing the second equation by the first, r5 = 16807
Taking the fifth root, r = 7.
The S6 = a*(r6 - 1)/(r - 1) = 21*(76-1)/(7-1) = 411768
The answer depends on what information you have been provided with.
Geometric series may be defined in terms of the common ratio, r, and either the zeroth term, a(0), or the first term, a(1).Accordingly,a(n) = a(0) * r^n ora(n) = a(1) * r^(n-1)
The summation of a geometric series to infinity is equal to a/1-rwhere a is equal to the first term and r is equal to the common difference between the terms.
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), ... } then the terms of the geometric series, T(n), are the sums of the first n terms and T(n) = a*(1 - r^n)/(1 - r). If |r| < 1 then T(n) tends to 1/(1 - r) as n tends to infinity.
Suppose the nth term is = arn where n = 1,2,3, ... Then the sum to the nth term is a*(rn+1 - 1)/(r - 1) or, equivalently, a*(1 - rn+1)/(1 - r)
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)
The answer depends on what information you have been provided with.
1/8
Geometric series may be defined in terms of the common ratio, r, and either the zeroth term, a(0), or the first term, a(1).Accordingly,a(n) = a(0) * r^n ora(n) = a(1) * r^(n-1)
the series can be 1,-4,16,-64
The summation of a geometric series to infinity is equal to a/1-rwhere a is equal to the first term and r is equal to the common difference between the terms.
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), ... } then the terms of the geometric series, T(n), are the sums of the first n terms and T(n) = a*(1 - r^n)/(1 - r). If |r| < 1 then T(n) tends to 1/(1 - r) as n tends to infinity.
The sum to infinity of a geometric series is given by the formula Sā=a1/(1-r), where a1 is the first term in the series and r is found by dividing any term by the term immediately before it.
The nth term of the series is [ 4/2(n-1) ].
The geometric sequence with three terms with a sum of nine and the sum to infinity of 8 is -9,-18, and 36. The first term is -9 and the common ratio is -2.
Brunelleschi is credited with being the first to use geometric principles for creating linear perspective.
In 2-dimensional geometry, the first shape circumscribesthe second while the second is inscribed in the first.