Question

What is the sum of the geometric series in which a1 = 7, r = 3, and an = 1,701?

Hint: Sn= a1(1-rn)/1-r, r ≠ 1, where a1 is the first term and r is the common ratio.

Answer 1

That formula basically gives it out. Just plug the numbers into the Sn formula.

Answer 2

So you have the geometric series formula:
\[S_{n} = a_{1} * \frac{ 1-r^{n} }{ 1-r }\]

a1 = 7
r = 4

I hope you know an = a1 * r^n so
an = 7 * (4^n)
an/7 = 4^n
\[\log _{4}(1701) = n\]

And plug a1, r, and n into that formula at the top.