Question

It is Arithmetic progression question.please solve this..​

Answer 1

Answer:

The money saved by Yasmeen for the first month is = Rs. 32

The money saved by Yasmeen for the second month is = Rs. 36

The money saved by Yasmeen for the third month is = Rs. 40

The total money she wants to save = Rs. 2000

So, by the given information:

a1 = 32, a2 = 36, a3 = 40, Sn = 2000.

Here, we will use the formula of finding the sum of n number of terms.

Sn = n/2 (2a + (n-1)d)

➜ 2000 = n/2 (2(32) + (n - 1)d)

➜ 2000 = n/2 (64 + (n - 1)4)

➜ 2000 = n/2 (64 + 4n - 4)

➜ 2000 = n/2 (60 + 4n)

➜ 2000 = n/2 × 4 (15 + n)

➜ 2000 = 2n (15 + n)

➜ 2000 = 30n + 2n²

➜ 2 (n² + 15n - 1000) = 0

➜ n² + 15n - 1000 = 0

➜ n² + 40n - 25n - 1000 = 0

➜ n (n - 40) - 15 (n + 40) = 0

➜ (n - 15)(n + 40) = 0

➜ n = 15,-40

Here, n represents the number of months in which she would be able to collect the money she want.

And as we know that number of months cannot be in negative, we omit the number -40.

So, the final answer here is : 15 months.

$\rule{200}2$