Question

How many terms of a GP $\frac{2}{3},\frac{-1}{3},\frac{1}{2}$..... should be added to get the sum equal to $\frac{55}{72}$?

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is C 5

Here, $a=\frac{2}{9},r=\frac{\frac{-1}{3}}{\frac{2}{9}}=\frac{-3}{2}$ and $Sn=\frac{55}{72}$
Since $Sn=\frac{a(1-r^n)}{1-r}$
$\frac{55}{72}=\frac{\frac{2}{9}\ast (1-{\left(\frac{-3}{2}\right)}^n)}{1-\left(\frac{-3}{2}\right)}$
$\Rightarrow \frac{275}{32}=1-(\frac{-3}{2}{)}^n$
$=1-\frac{275}{32}$
$={\left(\frac{-3}{2}\right)}^5$
$n=5$