Yasmeen saves Rs., 32 during the first month, | vedclass

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(D) Given that,Yasmeen's savings follow an arithmetic progression $(AP)$.First term $(a) = 32$.Common difference $(d) = 36 - 32 = 4$.Total savings $(S

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(D) Given that,Yasmeen's savings follow an arithmetic progression $(AP)$.First term $(a) = 32$.Common difference $(d) = 36 - 32 = 4$.Total savings $(S_n) = 2000$.The sum of the first $n$ terms of an $AP$ is given by the formula: $S_n = \frac{n}{2}[2a + (n - 1)d]$.Substituting the values: $2000 = \frac{n}{2}[2(32) + (n - 1)4]$.$2000 = \frac{n}{2}[64 + 4n - 4]$.$2000 = \frac{n}{2}[60 + 4n]$.$2000 = n(30 + 2n)$.$2000 = 30n + 2n^2$.Dividing by $2$: $n^2 + 15n - 1000 = 0$.Factoring the quadratic equation: $n^2 + 40n - 25n - 1000 = 0$.$n(n + 40) - 25(n + 40) = 0$.$(n + 40)(n - 25) = 0$.Since $n$ cannot be negative,$n = 25$.Therefore,she will save $Rs.\, 2000$ in $25$ months.

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 $Rs.\, 2000$?

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