Progressions : Sum of an A.P. Problem

Question

A gentleman buys every year Bank's cash certificates of value exceeding the last year's purchase by Rs. 300. After 20 years, he finds that the total value of the certificates purchased by him is Rs. 83,000. Find the value of the certificates purchased by him in the 13^th year.

1. Rs.4900
2. Rs.6900
3. Rs.1300
4. None of these.
   
   

Correct Choice is (1) and Correct Answer is Rs.4900

Explanatory Answer

Let the value of the certificates purchased in the first year be Rs. a.

The difference between the value of the certificates is Rs.300 (d = 300).

Since, it follows Arithmetic progression the total value of the certificates after 20 years is given by

S_n = = .

By simplifying, we get 2a + 5700 = 8300.

Therefore, a = Rs.1300.

The value of the certificates purchased by him in nth year = a + (n - 1) d.

Therefore, the value of the certificates purchased by him in 13th year = 1300 + (13 - 1) 300 = Rs.4900.

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