Question

In a infinite G.P. , the sum of first three terms is 70. If the extreme terms are multiplied by 4 and the middle term is multiplied by 5, the resulting terms form an A.p. then the sum to infinite terms of G.p.

• A. 120
• B. -40
• C. 160
• D. 80

Answer 1

Answer: (B)

-40

We have,

The three numbers be $a,aranda{r}^2$.

Given that,

$a+ar+a{r}^2=70$

$\Rightarrow a(1+r+r^2)=70......\left(1\right)$

Also given that,

$4a,5arand4a{r}^2$ in an A.P.

$\begin{align}

$\Rightarrow 2\left(5ar\right)=4a+4a{r}^2$

$\Rightarrow 5r=2+2r^2$

$\Rightarrow 2r^2-5r+2=0$

$\Rightarrow 2r^2-(4+1)r+2=0$

$\Rightarrow 2r^2-4r-1r+2=0$

$\Rightarrow 2r(r-2)-1(r-2)=0$

$\Rightarrow (r-2)(2r-1)=0$

$\Rightarrow r-2=0,2r-1=0$

$\Rightarrow r=2,r=\frac{1}{2}$

From (1) we get,

$a=10atr=2$

And $a=40atr=\frac{1}{2}$

Sum of this series

$=\frac{a}{1-r}$

$=\frac{40}{1-2}$

$=-40$

This is the answer.