Question

What is the common ratio of the geometric sequence below? –2, 4, –8, 16, –32, ...

Answer 1

Answer:

The common ratio of the geometric sequence is:

$r=-2$

Step-by-step explanation:

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

$a_n=a_1\cdot r^{n-1}$

where

• aₙ is the nth term

• a₁ is the first term

• r is the common ratio

Given the sequence

$-2,\:4,-8,\:16,\:-32,\:...$

Compute the ratios of all the adjacent terms:  $r=\frac{a_n+1}{a_n}$

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

The ratio of all the adjacent terms is the same and equal to

$r=-2$

Therefore, the common ratio of the geometric sequence is:

• $r=-2$