Question

Find the common ratio for the following sequence.1/2, -1/4, 1/8, -1/16, ...A. 1/2B. -2C. -1/2D. 2There is a picture too if you need it.

Answer 1

Consider the given series,

`(1)/(2),(-1)/(4),(1)/(8),(-1)/(16),\ldots`

Observe that the given series is a geometric progression, since the ratio is constant throughout,

`r=(a_2)/(a_1)=(a_3)/(a_2)=(a_4)/(a_3)`

Solve for the common ratio as,

`r=(a_2)/(a_1)=((-1)/(4))/((1)/(2))=(-1)/(4)*(2)/(1)=(-1)/(2)`

Thus, the common ratio of the series is -1/2.