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

Answer:

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

$a_n=-4\cdot \:2^{n-1}$      

Thus, option (A) is true.

Step-by-step 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

$\frac{-8}{-4}=2,\:\quad \frac{-16}{-8}=2,\:\quad \frac{-32}{-16}=2$

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.