We have asked to calculate the number of months Yasmeen required to save Rs 2000 if she saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month and she continues to save in this manner ?

ML Aggarwal Avichal Publication

Arithmetic Progression Chapter 9 Question no 24

## Clearly saving of Yasmeen forms an AP with first term a=32 and common difference d=36−32=4.

Let it take n months to saves Rs. 2000.

∴Sn=2n[2a+(n−1)d]=2000

⇒2n[2×32+(n−1)×4]=2000

⇒n[2n+30]=2000

⇒n[n+15]=1000

⇒n2+15n−1000=0

⇒(n+40)(n−25)=0

⇒n=−40,25

But n=-40 being negative integer is not possible.

∴n=25

Hence, it takes 25 months for Yasmeen to saves Rs.2000.