Question

A man borrows Rs 8000 and agrees to repay with a total interest of Rs. 1360 in 12 monthly instalments.Each instalment being less than the preceding one by Rs.40 .Find the amount of the first and last term​

Answer 1

$\sf{\underline{Given:}}$

Money (man borrows): 8000

Interest (he will pay): 1360

Money he will pay:

$\implies$ 8000 + 1360

$\implies$ 9360

$\sf{\underline{Now:}}$

He will pay in 12 installments.

$\sf{\underline{Note:}}$ With a difference of 40 in each installment.

$\sf{\underline{This\:is\:a\:form\:of\:AP.}}$

$\sf{\underline{Where:}}$

Common difference (d) = -40

Number of terms (n) = 12

Sum of 12 terms (Sum) = 9360

$\sf{\underline{So:}}$

Sum of n terms in AP is:

$\boxed{\sf{Sum = \frac{n}{2} [2a + (n - 1)d]}}$

$\implies$ $9360 = \frac{12}{2} [2a - 40(12 - 1)]$

$\implies$ $9360 = \frac{12}{2} [2a - 40(11)]$

$\implies$ $9360 = 6(2a - 440)$

$\implies$ $1560 = 2a - 440$

$\implies$ $2a = 2000$

$\implies$ $a = \frac{2000}{2}$

$\implies$ $a = 1000$

nth term in AP is given by:

$\boxed{\sf{a(n) = a + (n - 1)d}}$

$\sf{\underline{Last\:term:}}$

$\implies$ $1000 - 40(12 - 1)$

$\implies$ $1000 - 40(11)$

$\implies$ $1000 - 440$

$\implies$ $560$

$\sf{\underline{Therefore:}}$

First installment: 1000

Last one: 560