Question

Vijay invests some amount in 'National saving certificate'. For the $1^{st}$ year he invests Rs. 500, for the $2^{nd}$ year he invests Rs. 700, for the $3^{rd}$ year he invests Rs. 900, and so on. How much amount he has invested in 12 years?

• A. 18600
• B. 19200
• C. 15400
• D. 15600

Answer 1

The correct option is B 19200

The investment done by vijay in each year is as follows $500,700,\mathrm{900........}$
This sequence makes an AP with first term $a=500$, common difference $d=200$
Given, number of terms $n=12$
Since,

$\Rightarrow S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$\Rightarrow S_{12}=\frac{12}{2}[2\times 500+(12-1\left)200\right]$

$\Rightarrow S_{12}=6[1000+2200]$
$\Rightarrow S_{12}=19200$
$\therefore$ vijay's total investment in 12 years $S_{12}=19200$