Answer:
[tex]\text{The next three terms of G.P is }\frac{1}{2}, \frac{-1}{8}, \frac{1}{32}[/tex]
Step-by-step 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
[tex]a, ar, ar^2, ar^3, ar^4,...[/tex]
where a and r are the first term and common ratio.
[tex]a=-2, r=\frac{-1}{4}[/tex]
[tex]\text{Second term=}ar=-2\times (\frac{-1}{4})=\frac{1}{2}[/tex]
[tex]\text{Third term=}ar^2=-2\times (\frac{-1}{4})^2=\frac{-1}{8}[/tex]
[tex]\text{Fourth term=}ar^3=-2\times (\frac{-1}{4})^3=\frac{1}{32}[/tex]
[tex]\text{The next three terms of G.P is }\frac{1}{2}, \frac{-1}{8}, \frac{1}{32}[/tex]
