Given geometric sequence tn. Find S13 if t1=5 , r=2.

Answer 1

A geometric sequence has the form:

t_n = t₁·r^n-1

For t₁ = 5 and r = 2:

t_n = 5·2^n-1

S13 is the sum of the first 13 terms. The formula for the sum is:

S = t₁·(1-rⁿ) / (1-r)

In your problem, t₁ = 5, r = 2, n = 13. Plug in the numbers and use your calculator to help compute the answer.

Answer 2

The sum of the first n terms of a geometric sequence tn is given by Sn=(t1*(1-r^n))/(1-r) where t1 is the first term of the sequence and r is the common multiple. In this case t1=5, r=2, and because we want the sum of the first 13 terms n=13. Substituting gives S13=(5(1-2^13))/(1-2)=(-5(1-2^13)).

This is an exact answer. If you're doing this problem on MyMathLab or similar then you may need to simplify further with the help of a calculator.

Answer 3

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