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]