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.