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Question
A farmer borrows Rs.1,000 and agrees to repay with a total interest of Rs. 140 in 12 installments, each installment being less that the preceding installment by Rs. 10. What should be his first installment?
Solution
As each installment being less that the preceding installment by Rs. 10 the
installments are in A.P.
S12 = 1000 + 140 = 1140
n = 12, d = −10
`s_n=n/2[2a+(n-1)d]`
`s_12=12/2[2a+(11)(-10)]`
`1140=6[2a-110]`
`1140/6=[2a-110]`
190 = [2a − 110]
2a = 190 + 110
2a = 300
a = `300/2`
a = 150
The first installment = Rs. 150.
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