What is the 6th term of the geometric sequence where a1 = - 4,096 and a4 = 64?

Question

Abbie Frost

Mathematics

11 January, 15:17

What is the 6th term of the geometric sequence where a1 = - 4,096 and a4 = 64?

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Answers (1)

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Damian Esparza · Answer 1

First, we need to solve for the common ratio from the data given by using the equation.

a (n) = a (1) r^ (n-1)

64 = - 4096r^ (4-1)

64 = - 4096r^3

r = - 1/4

Then, we can find the 6th term as follows:

an = - 4096 r^ (6-1)

an = - 4096 (-1/4) ^5

an = 4