Question

Consider the series given below.

Answer 1

Answer:

n = 8

Step-by-step explanation:

This is a geometric sequence where the sum to n terms is

$S_{n}$ = $\frac{a(r^n-1)}{r-1}$

where a is the first term and r the common ratio

r = 6 ÷ 2 = 18 ÷ 6 = 54 ÷ 18 = 3 and a = 2, thus

$\frac{2(3^n-1)}{3-1}$ = 6560

$\frac{2(3^n-1)}{2}$ = 6560 ← cancel the 2

$3^{n}$   - 1 = 6560 (add 1 to both sides )

$3^{n}$ = 6561

note that 6561 = $3^{8}$, hence

$3^{n}$ = $3^{8}$ ⇒ n = 8