Question

A student Arun saves Rs. $32$ from his pocket money during the first month, Rs. $36$ in the second and Rs. $40$ in the third month. If he continues to save in this manner, in how many months will he save Rs. $2000$? Also, write what value is depicted in this question.

Answer 1

Given, In first month$\to 32$

In second month$\to 36$

In third month$\to 40$

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

$S_n=2000$

$2000=\frac{n}{2}[64+(n-1\left)4\right]$

$2000=\frac{n}{2}[64+4n-4]$

$2000=\frac{n}{2}[60+4n]$

$4000=60n+4n^2$

$1000=15n+n^2=1n^2+15n-1000=0$

$\therefore$The value of 'n' would get $\sim 14$ months