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 ?

Explanation

Given that,
Yasmeen, during the first month, saves = Rs. 32
During the second month, saves = Rs. 36
During the third month, saves = Rs. 40
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
and she saves total money, i.e., `S_(n)` = Rs. 2000
We know that, sum of first n terms of an AP is,
` " " S_(n)= (n)/(2)[2a+(n-1)d]`
`implies 2000= (n)/(2)[2xx32+(n-1)xx4]`
`implies 2000=n(32+2n-2)`
`implies 2000=n(30+2n)`
` implies 1000=n(15+n)`
`implies 1000=15n+n^(2)`
`implies n^(2)+15n-1000=0`
`implies n^(2)+40n-25n-1000=0`
`implies n(n+40)-25(n+40)=0implies(n+40)(n-25)=0`
` :. " " n=25 " " [:' n ne -40]`
Hence, in 25 month will she save Rs. 2000. ` " " ` [since, month cannot be negative]