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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 the 30th installment?

$The\;first\;installment\;of\;the\;loan\;is\;Rs\;100.\\* The\;second\;installment\;of\;the\;loan\;is\;Rs\;105\;and\;so\;on.\\* The\;amount\;that\;the\;man\;repays\;every\;month\;forms\;an\;A.P.\\* The\;A.P\;is\;100,105,110,...\\* First\;term,\;a=100,\;common\;difference\;d=5\\* \therefore a_{30}=a+(30-1)d=100+(29)(5)=100+145=245\\* Thus,\;the\;amount\;to\;be\;paid\;in\;the\;30^{th}\;installment\;is\;Rs\;245.$