What is the recursive formula for this geometric sequence?

Question

-4, -24, -144, -846, ...

A) {A₁ = -4

{A_n = a_n-1 x 6

B) {A₁ = -4

{A_n = a_n-1 x 30

C) {A₁ = -6

{A_n = a_n-1 x 4

D) {A₁ = -6

{A_n = a_n-1 x 30

Answer 1

-24 / -4 = 6

-144 / -24 = 6

Which choice has a common ratio of 6?

Answer 2

The correct answer is A.

The first value of the sequence (A₁) is -4, so you can immediately narrow down the answer choices to A and B. Since you have specified that this is a geometric sequence, the common ratio, which is the amount you need to multiply A_n-1 to get to A_n, is the same for every two consecutive numbers. You can start with the first two. You know that A₂ = -24 and A₁ = -4, and you can substitute these two values to find the common ratio.

(-24) = (-4) * x

x = (-24)/(-4)

x = 6

This means that the common ratio is 6, and the answer is A.