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, Sn = 
[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