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

= 2

Step-by-step explanation:

The n th term of a geometric sequence is

= a

where a is the first term and r the common ratio

Given

= - 8, then ar = - 8 → (1)

Given

= 512, then a = 512 → (2)

Divide (2) by (1)

= , thus

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

r = = - 4

Substitute r = - 4 into (1)

a(- 4) = - 8

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

a = 2

Thus

= 2

(x+3)(x+7)

step-by-step explanation: