Question:
A man starts repaying a loan as first installment of Rs. 100 . If he increases the installment by Rs 5 every month, what amount he will pay in the $30^{\text {th }}$ installment?
Solution:
The first installment of the loan is Rs 100.
The second installment of the loan is Rs 105 and so on.
The amount that the man repays every month forms an A.P.
The A.P. is 100, 105, 110, …
First term, a = 100
Common difference, d = 5
$\mathrm{A}_{30}=a+(30-1) d$
$=100+(29)(5)$
$=100+145$
$=245$
Thus, the amount to be paid in the $30^{\text {th }}$ installment is Rs 245 .