Find the sum s n = a 1 + ... + a n. s n = a 1 + ... + a n of the first n n terms of the series 7 , 21 , 63 , 189 , ... 7 , 21 , 63 , 189 , ...

Question

Find the sum  of the first  terms of the series . (The answer is a function of . Check your answer with .)

Answer 1

This is a geometric appears to be a geometric series with r=3 and a₁=7.

The sum is 7(3ⁿ⁺¹-1)/2,

If you don't know this directly, you can derive it from:

S=a₁(1 + r + r² + .... + rⁿ)

Multiply both sides by r and add the two series to get the desired result.