Question

Find the common ratio of the geometric sequence minus, 16, comma, 32, comma, minus, 64, comma, dot dot dot−16,32,−64,...
Answer
Attempt

Answer 1

To find the common ratio of a geometric sequence, you can divide any term in the sequence by the term that comes before it.

In the given sequence: \(-16, 32, -64, \ldots\)

Let's calculate the common ratio:

1. To find the ratio between the second term (32) and the first term (-16):
\[
r = \frac{\text{second term}}{\text{first term}} = \frac{32}{-16} = -2
\]

2. Now, to confirm that this is consistent throughout the sequence, calculate the ratio between the third term (-64) and the second term (32):
\[
r = \frac{\text{third term}}{\text{second term}} = \frac{-64}{32} = -2
\]

Since both calculations yield the same common ratio, we conclude:

The common ratio of the geometric sequence is \(-2\).

Answer 2

Find the common difference of the arithmetic sequence 19, comma, 27, comma, 35, comma, dot dot dot19,27,35,...