Aman arrange stop ay off a debt of Rs.3600 by 40 annual installments which for man arithmetic series. When 30 of the installments are paid, he dies leaving one - third of the debt unpaid, find the value of the first installment.

Given, Total amount of payable in 40 annual installments, S₄₀ = 3600

After 30 installment he died and leaving of the debt unpaid

Which means, total in 30 installment, S₃₀= of the debt

S₃₀= * 3600 = 2400

We know sum of n terms, S_n = [2a + (n – 1) d]

For 30 installments, S₃₀ = [2a + (30 – 1) d]

2400 = 15 [2a + 29d]

160 = 2a + 29d

2a = 160 – 29d

a = (i)

For 40 installments, S₄₀ = [2a + (n – 1) d]

3600 = [2a + (40 – 1) d]

180 = 2a + 39d

2a = 180 – 39d

a = (ii)

From (i) and (ii), we get

=

160 – 29d = 180 – 39d

39d – 29d = 180 – 160

10d = 20

d = 2

Putting the value of d in (i), we get

a =

= = = 51

Hence, value of first installment is 51