An important question from arithmetic progression chapter in which we have to find the value of the first instalment if a man arranges to pay off a debt of Rs.3600 in 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid he dies leaving one-third of the debt unpaid.

Book – RS Aggarwal, Class 10, chapter 5C, question no 47.

## Debt ofÂ Rs.3600Â is to be paid onÂ 40Â annual installments.

âˆ´S40â€‹=3600........(i)

AfterÂ 30Â installmentsÂ 31â€‹Â of the debt is unpaid

âˆ´S30â€‹=3600âˆ’ 1/3ofÂ 3600

Â Â Â Â =3600âˆ’1200

Â S30â€‹=2400â€‹

in (i) we get.

S40â€‹=40/2â€‹[2a+39d]=360

â‡’2a+39d=180â€‹……(iii)

in (ii)

S30â€‹=2400

â‡’30/2â€‹[2a+29d]=2400

â‡’2a+29dâ€‹=2400……(iv)

(iii)âˆ’(iv)

10dâˆ’=20

â‡’d=2â€‹

âˆ´2a=180âˆ’39d

Â Â Â Â Â Â Â =180âˆ’39Ã—2

Â Â Â Â Â Â Â =180âˆ’78

Â Â Â Â Â Â Â =2a=102

Â Â Â Â Â Â Â â‡’a=102â€‹/2

Â Â Â Â Â Â Â Â Â Â

Â Â Â Â Â Â â‡’a=51â€‹ value of first installment