Q. 354.2( 9 Votes )

# Yasmeen 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 2000?

Answer :

Given that,

Yasmeen, during the first month, saves = 32 Rs

During the second month, saves = 36 Rs

During the third month, saves = 40 Rs

Let Yasmeen saves Rs 2000 during the n months.

Here, we have arithmetic progression 32, 36, 40, …

First term, a = 32

common difference, d = 36 – 32 = 4

Total money save by her in n months = Sum of this AP upto n terms

4000 = n[ 2(32) + (n - 1)4]

4000 = n[ 64 + 4n - 4)

4000 = n[ 4n + 60]

4n^{2} + 60n - 4000 = 0

n^{2} + 15n - 1000 = 0

n^{2} + 40n - 25n - 1000 = 0

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

n = 25 or n = - 40

but n = - 40 as no of terms and months cannot be negatice

so it would take 25 months to save 2000 Rs.

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The sum of n terms of an A.P. is 3n^{2}+ 5n. Find the A.P. Hence, find its 16th term.