Question

A geometric sequence is shown below.

Answer 1

Answer:

An explicit representation for the nth term of the sequence:

$f_n=-\frac{1}{2}\cdot \:4^{n-1}$

It means, option (B) should be true.

Step-by-step explanation:

Given the geometric sequence

$-\frac{1}{2},\:-2,\:-8,\:-32,...$

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

$f_n=f_1\cdot r^{n-1}$

Determining the common ratios of all the adjacent terms

$\frac{-2}{-\frac{1}{2}}=4,\:\quad \frac{-8}{-2}=4,\:\quad \frac{-32}{-8}=4$

As the ratio is the same, so

r = 4

Given that f₁ = -1/2

substituting r = 4, and f₁ = -1/2 in the nth term

$f_n=f_1\cdot r^{n-1}$

$f_n=-\frac{1}{2}\cdot \:4^{n-1}$

Thus, an explicit representation for the nth term of the sequence:

$f_n=-\frac{1}{2}\cdot \:4^{n-1}$

It means, option (B) should be true.