A man arranges to pay a debt of Rs.3600 in 40 monthly instalments which are in a AP. When 30 instalments are paid he dies leaving one third of the debt unpaid. Find the value of the first instalment.
Ans: Let the value of I instalment be x S_{40} = 3600.
⇒ 40/2 [2a + 39d ]=3600
⇒2a + 39d = 180 - 1
S_{30} = 30/2 [2a + 29d ]=2400
⇒30a + 435d = 2400
⇒2a + 29d = 160 - 2
Solve 1 & 2 to get
d = 2 a = 51.
∴ I instalment = Rs.51.