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
         Â
      ⇒a=51​ value of first installment