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# 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 his $30^{th}$ installment?

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• $n^{th}$ term of an $A.P.=t_n=a+(n-1)d$
Given that the first installment is $Rs.100$
Each installment is increased by $Rs.5$
$\therefore$ The amount repaid by the man in each month is given by
$100,105,110,115,...........$ respectively.
This sequence is A.P. with first term $=a=100$ and common difference $=d=5$
The $30^{th}$ installment=$30^{th}$ term in this sequence.
We know that $n^{th}$ term of an A.P.=$t_n=a+(n-1)d$
$i.e., t_{30}=a+(30-1)d=100+29\times 5=245$
$\therefore$ The amount paid by the man in the $30^{th}$ installment=$Rs.245$
answered Feb 24, 2014