Question

What is the common ratio of the sequence $2$, $-4$, $8$, $-16$, $32$, ...?

A) $-2$
B) $2$
C) $-4$
D) $4$

Answer 1

Option (A), The common ratio of the sequence $2$, $-4$, $8$, $-16$, $32$, ... is -2, because each term after the first is produced by multiplying the preceding term by -2.

Step-by-step explanation:

To find the common ratio of the given sequence, we should divide any term in the sequence by the term preceding it. For example, we could divide the second term (-4) by the first term (2), or the third term (8) by the second term (-4), and so on. Doing this, we get:

• -4 / 2 = -2
• 8 / -4 = -2
• -16 / 8 = -2
• 32 / -16 = -2

All these divisions result in -2, which means that the common ratio of the sequence is -2. The sequence is a geometric sequence because each term is the previous term multiplied by the common ratio (-2).