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 of Rs.3600 is to be paid on 40 annual installments.

∴S40=3600........(i)

After 30 installments 31 of the debt is unpaid

∴S30=3600− 1/3of 3600

=3600−1200

S30=2400

in (i) we get.

S40=40/2[2a+39d]=360

⇒2a+39d=180……(iii)

in (ii)

S30=2400

⇒30/2[2a+29d]=2400

⇒2a+29d=2400……(iv)

(iii)−(iv)

10d−=20

⇒d=2

∴2a=180−39d

=180−39×2

=180−78

=2a=102

⇒a=102/2

⇒a=51 value of first installment