Question

Devendra invested in a national saving certificate scheme. In the first year he invested Rs.$1000$ in second year Rs.$1400$, in the third year Rs.$1800$ and so on. Find the total amount that he invested in $12$ years.

Answer 1

Devendra invested Rs.$1,000$ in the first year and Rs.$1,400$ in the second year.'Again in the third year he invested Rs.$1800$.
Thus his investment in each year forms an A.P.
Consider the A.P $1000,1400,1800,......$
Here $a=1000$ and common difference $=1400-1000=1800-1400=400$
Sum of total amount Devendra invested $=S_n$
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$\Rightarrow$ $S_{12}=\frac{12}{2}[2\times 1000+(12-1)\times 400]$
$\Rightarrow$ $S_{12}=6[2000+11\times 400]$
$\Rightarrow$ $S_{12}=6[2000+4400]$
$\Rightarrow$ $S_{12}=$ Rs.$38,400$
Thus, the total amount he invested in 12 years is Rs.$38400$.