Question

The first term of a geometric sequence is –2 and the common ratio is -1/4 . What are the next three terms of the sequence

Answer 1

well -2(-1/4) is .5

so -2, .5,(multiply each by -1/4)

-2, 0.5, -0.125, 0.03125

Answer 2

`\text{The next three terms of G.P is }(1)/(2), (-1)/(8), (1)/(32)`

Explanation:

Given that the first term of a geometric sequence is -2 and the common ratio is -1/4.

we have to find the next three terms of the sequence.

The geometric sequence can be written as

`a, ar, ar^2, ar^3, ar^4,...`

where a and r are the first term and common ratio.

`a=-2, r=(-1)/(4)`

`\text{Second term=}ar=-2* ((-1)/(4))=(1)/(2)`

`\text{Third term=}ar^2=-2* ((-1)/(4))^2=(-1)/(8)`

`\text{Fourth term=}ar^3=-2* ((-1)/(4))^3=(1)/(32)`

`\text{The next three terms of G.P is }(1)/(2), (-1)/(8), (1)/(32)`