2) A man borrows RS.800installment being less than the preceding one b

1.	2) A man borrows RS.800installment being less than the preceding one by Rs. 40. Find the amount of first and lastO and agrees to repay with a interest of RS. 1360 in 12 monthlyinstallment
Answer» Money he borrows = 8000 Interest he will pay = 1360 Total money he will pay after = 8000 + 1360 = 9360 Now he will pay in 12 installments with a difference of 40 in each installment. This is a form of AP, where common difference d = -40, number of terms n = 12, and sum of 12 terms is 9360 So, Sum of n terms in AP is Sum = n/2 [ 2a + (n - 1)d ] 9360 = 12/2 [ 2a - 40(12 - 1) ] 9360 = 6 [ 2a - 440 ] 1560 = 2a - 440 2a = 2000 a = 1000 nth term in AP is given by: a(n) = a + (n - 1)d Last term = 1000 - 40(12 - 1) =1000 - 440 = 560 Therefore first installment is 1000 and last one is 560

2) A man borrows RS.800installment being less than the preceding one by Rs. 40. Find the amount of first and lastO and agrees to repay with a interest of RS. 1360 in 12 monthlyinstallment

Answer»

Money he borrows = 8000

Interest he will pay = 1360

Total money he will pay after = 8000 + 1360 = 9360

Now he will pay in 12 installments with a difference of 40 in each installment.

This is a form of AP,

where common difference d = -40, number of terms n = 12, and sum of 12 terms is 9360

So,

Sum of n terms in AP is

Sum = n/2 [ 2a + (n - 1)d ]

9360 = 12/2 [ 2a - 40(12 - 1) ]

9360 = 6 [ 2a - 440 ]

1560 = 2a - 440

2a = 2000

a = 1000

nth term in AP is given by:

a(n) = a + (n - 1)d

Last term = 1000 - 40(12 - 1)

=1000 - 440 = 560

Therefore first installment is 1000 and last one is 560