Find the sum of the first 7 terms of the following series, to the nearest integer.

15,3, 3/5

19

Step-by-step explanation:

This is a geometric series.

15, 3, (3/5), ...

common ratio r = 3/15 = (1/5)

a_1 = 15

Formula for nth term: a_n = a_1 * r^ (n-1)

a_n = 15 * (1/5) ^ (n - 1)

We want the sum of the first 7 terms.

S = a_1 * (r^n - 1) / (r - 1)

here let n = 7

S = 15 * ((1/5) ^7 - 1) / ((1/5) - 1)

S = 15 * ((1/5) ^7 - 1) / (-4/5)

S = 15 * (5/-4) * ((1/5) ^7 - 1)

S = (-75/4) * (-0.9999872)

S = - (-18.74976) = 18.749 ...

The sum is about 19