Question

What is the next term in the sequence below?

-324,108,-36,12...
a) –4
b) –3
c) 3
d) 4

Answer 1

A because it is just dividing by -3.

Answer 2

option a is correct

The next term in the sequence -324, 108, -36, 12,..... is -4

Explanation:

In Geometric sequences it follows a pattern where the next term is found by multiplying by a constant i,e common ration(r)

For
`a_1, a_2, a_3, a_4, a_5, ....`

Common ratio(r) =
`(a_2)/(a_1)=(a_3)/(a2) =(a_4)/(a_3)...`

the formula for nth term of this sequence is given by;

`a_n = a_1r^(n-1)`

Given the sequence: -324, 108, -36, 12,.....

This sequence is a geomtric sequence with common ratio =
`-(1)/(3)` and
`a_1 = -324`

Since,

`(a_2)/(a_1) = (108)/(-324) = -(1)/(3)`,

`(a_3)/(a_2) = (-36)/(108) = -(1)/(3)` and so on..

We have to find the next term in this sequence i.e,
`a_5`

Using nth sequence formula:

`a_5= -324(-(1)/(3))^(5-1) = -324(-(1)/(3))^(4) = -324 * (1)/(81)= -4`

Therefore, the next term in the sequence -324, 108, -36, 12,..... is -4