Find the 5th term of a GP. 9, —6, 4, .... - Vidyadip

Question

Find the 5th term of a GP. 9, —6, 4, ....

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Answer

Here, $a=9$ and $r=\frac{-6}{9}=\frac{-2}{3} .$ The 5 th term is to be found, so $n=5$
Putting values of $a, r$ and $n$ in the general term $\mathrm{T}_{n}=a r^{n-1}$, we get
$ \begin{aligned} \mathrm{T}_{5} &=9 \times\left(\frac{-2}{3}\right)^{5-1} \\ &=9 \times\left(\frac{-2}{3}\right)^{4} \\ &=9 \times \frac{16}{81} \\ &=\frac{16}{9} \end{aligned} $
Hence, the 5 th term of the G. P. is $\frac{16}{9}$.

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