Question

Find the sum of the first fifteen terms of the series:

Answer 1

Answer:

Step-by-step explanation:

The given series is a geometric series because the consecutive terms differ by a common ratio. The formula for determining the sum of the first n terms, Sn of a geometric sequence is expressed as

Sn = (ar^n - 1)/(r - 1)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

a = 3

r = 6/3 = 12/6 = 2

n = 15

Therefore, the sum of the first 15 terms, S15 is

S15 = (3 × 2^(15) - 1)/2 - 1

S15 = (3 × 32767)/1

S15 = 98301