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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 certicates purchased by him
- in the first year
- in the eight year



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Let the value of first certificate = Rs x
each year, it the value is increased by 100. So the prices of the certificate forms an A.P. with common difference 100
So first term,a=x, common difference,d = 100
In 10 years, he will have 10 cards.
So n=10

S_n= \frac{n}{2}(2a+(n-1)d)  \\  \\ S_1_0= \frac{10}{2}(2x+(10-1)100)=54500 \\  \\ 5(2x+9*100)=54500 \\  \\ 10x+4500=54500 \\  \\ 10x=54500-4500=50000 \\  \\ x= \frac{50000}{10}=Rs.\ 5000

a. Value of first certificate = Rs. 5000
b. For eighth year, n=8
   value = 5000+(8-1)100 = Rs. 5700

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The value of certicates purchased by him in the first year is Rs 5000. And in 8 year is Rs 5700.
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