Question

A man has saved $Rs.640$ during the first month, $Rs.720$ in the second month and $Rs.800$ in the third month. If he continues his savings in this sequence, what will be his savings in the ${25}^{th}$ month?

Answer 1

It is given that a man saved Rs.$640$ during the first month, Rs.$720$ in the second month and Rs.$800$ in the third month.

Let us write his savings like a sequence as follows: $640,720,800,......$ where the first term is $a_1=640$, second term is $a_2=720$ and so on.

We find the common difference $d$ by subtracting the first term from the second term as shown below:

$d=a_2-a_1=720-640=80$

We know that the general term of an arithmetic progression with first term $a$ and common difference $d$ is $T_n=a+(n-1)d$

To find his savings in the $25$th month, we have to find the $25$th term of the A.P, substitute $n=25,a=640$ and $d=80$ in $T_n=a+(n-1)d$ as follows:

$T_{25}=640+(25-1)80=640+(24\times 80)=640+1920=2560$

Hence, the man saved Rs.$2560$ in the $25$th month.