Question

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -8 and 512

Answer 1

Answer:

$a_{n}$ = 2$(-4)^{n-1}$

Step-by-step explanation:

The n th term of a geometric sequence is

$a_{n}$ = a$(r)^{n-1}$

where a is the first term and r the common ratio

Given

$a_{2}$ = - 8, then ar = - 8 → (1)

Given

$a_{5}$ = 512, then a$r^{4}$ = 512 → (2)

Divide (2) by (1)

$\frac{ar^4}{ar}$ = $\frac{512}{-8}$, thus

r³ =- 64 ( take the cube root of both sides )

r = $\sqrt[3]{-64}$ = - 4

Substitute r = - 4 into (1)

a(- 4) = - 8

- 4a = - 8 ( divide both sides by - 4 )

a = 2

Thus

$a_{n}$ = 2$(-4)^{n-1}$