UPSC CDS 2 2021 Math Paper

Given,
A person saves ₹1000 more than he did the previous year.
Savings in the first year is ₹2000.
The given problem forms the following AP,
AP: 2000,3000,4000,...
First term, a=2000
Common difference,
d=3000−2000=1000
Sum of n terms, Sn=170000
We know, Sn=‌

n

2

[2a+(n−1)d]
⇒‌‌‌

n

2

[2a+(n−1)d]=170000
⇒‌

n

2

[2×2000+(n−1)(1000)]
=170000
⇒n[4000+(n−1)(1000)]=340000
⇒n[4+(n−1)]=340
⇒‌‌n(n+3)=340
⇒n2+3n−340=0
⇒n2+20n−17n−340=0
⇒n(n+20)−17(n+20)=0
⇒‌‌(n+20)(n−17)=0
Hence, the person saves ₹170000 in 17 yr.