On 1st Jan every year person buys NSC certificate of value exceeding that of his last year purchase by Rs 100. After 10 years he finds that the total value of the certificates held by him is Rs 54500. Find the value of the certificates purchased by him - in the first year - in the eighth year

Answers (1)

Let the value of the first certificate be Rs. x
Every year it's value is increased by Rs.100.
Which means the prices of the certificate forms an A.P. with common difference 100
First term (a)=x
Common difference (d)=100
In n=10 years he will be having 10 cards.
The formula to solve this A.P. is
S_n=fracn2(2a+(n-1)d)
S_10=frac102(2x+(10-1)100)=54500
5(2x+9*100)=54500
10x+4500=54500
10x=54500-4500=50000
x=frac5000010=Rs.5000

  1. Value of the first certificate is=Rs. 5000
  2. For Eighth  year,n=8 value=5000+(8-1)*100=Rs.5700

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