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