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 ${30}^{th}$ installment?

Answer 1

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 $d=5$
$\therefore a_{30}=a+(30-1)d=100+\left(29\right)\left(5\right)=100+145=245$
Thus, the amount to be paid in the ${30}^{th}$ installment is Rs. $245$.