**Q) **Prerna saves Rs. 32 during the first, month, Rs. 36 in the second month and Rs. 40 in the third month. if she continues to save in this manner, in how many months will she save Rs. 2,000?

**Ans: **

From the given data, we get AP as,

32, 36, 40, …..

Let’s consider that Prerna takes n months to save total of Rs. 2,000

Hence, S_{n }= 2000

We know that sum of n terms of an A.P. S_{n }= (2a + (n-1) d)

2000_{ }= (2 x 32 + (n-1) 4)

or 4000 = n (4n + 60)

or 4n^{2} + 60n – 4000 = 0

or n^{2} + 15n – 1000 = 0

(n + 40) (n -25) = 0

Since n ≠ -40; hence, n = 25

**Therefore, Prerna will take 25 months to save Rs. 2,000**