Question

A man starts repaying a loan as first instalment of $\text{Rs}.100.$ If he increases the instalment by $\text{Rs}.5$ every month, then what amount he will pay in the ${30}^{th}$
instalment?

Answer 1

First instalment of the loan is $\text{Rs}.100.$
The second instalment of the loan is $\text{Rs}.105$ and so on as the instalment increases by $\text{Rs}.5$ every month.
Thus, the amount that the man repays every month forms an A.P.
Thus, A.P. is $100,105,110,...$
Here, first term, $a=100$ and common difference, $d=5$
As we know, $a_n=a+(n-1)d$
So, the ${30}^{th}$ term in this A.P will be
$a_{30}=a+(30-1)d$
$\Rightarrow a_{30}=100+\left(29\right)\left(5\right)$
$\Rightarrow a_{30}=100+145$
$\therefore a_{30}=245$

Final answer: Hence, the amount to be paid in the ${30}^{th}$ installment will be $\text{Rs}.245$.