Question

The first terms of a $G.P.$ is $27$ and its $8^{th}$ term is $\frac{1}{81}$. Find the sum of its first $10$ terms.

Answer 1

Solution:-

first term of g.p = 97

$8^{th}$ term of G.P $=9r^7=\frac{1}{81}$

$27r^7=\frac{1}{81}$

$r^7=\frac{1}{21\times 27}$

$r=\frac{1}{3}$

Sum of first 10 term of g.p = $\frac{a(1-r^{10})}{1-r}$

$=\frac{27.(1-(\frac{1}{3}{)}^{10})}{1-\frac{1}{3}}$

$=40.4993$