Question

Find an explicit rule for the nth term of the sequence.

-4, -8, -16, -32, ...

A) an = -4 • 2n - 1
B) an = 2 • -4n + 1
C) an = 2 • -4n
D) an = -4 • 2n

Answer 1

An explicit rule for the nth term of the sequence will be:

`a_n=-4\cdot \:2^(n-1)`

Thus, option (A) is true.

Explanation:

Given the sequence

`-4, -8, -16, -32, ...`

A geometric sequence has a constant ratio r and is defined by

`a_n=a_0\cdot r^(n-1)`

Computing the ratios of all the adjacent terms

`(-8)/(-4)=2,\:\quad (-16)/(-8)=2,\:\quad (-32)/(-16)=2`

As the ratio 'r' is the same.

so

`r=2`

as

`a_1=-4`

Hence, the nth term of the sequence will be:

`a_n=a_0\cdot r^(n-1)`

substituting the values
`r=2` and
`a_1=-4`

`a_n=-4\cdot \:2^(n-1)`

Therefore, an explicit rule for the nth term of the sequence will be:

`a_n=-4\cdot \:2^(n-1)`

Thus, option (A) is true.