Permutations and Combinations

Permutations and Combinations

Question

A man buys every year Bank’s cash certificates of value exceeding the last year purchase by Rs. 25. After 20 years, he finds that the total value of the certificates purchased by him is Rs. 7250. Find the values of the certificates purchased by him

(i) In the first year. (ii) In the 13th year.

Answer

Let Rs. a be the value of the certificates purchased by him in the first year and Rs. d be the value of the certificate in excess every year.
∴                  d = Rs. 25
Since the value of the certificates purchased by him after 20 years  = 7250
∴              straight S subscript 20 space equals space 7250
rightwards double arrow       20 over 2 left square bracket 2 left parenthesis straight a right parenthesis space plus space left parenthesis 20 minus 1 right parenthesis 25 right square bracket space equals space 7250
                                                          open curly brackets By space using space straight S subscript straight n space equals space straight n over 2 left parenthesis 2 straight a plus top enclose straight n minus 1 end enclose straight d close curly brackets
space space space rightwards double arrow space space space space space space space space space 10 left square bracket 2 straight a space plus space 475 right square bracket space space equals space 7250
rightwards double arrow                   2a + 475 = 725   rightwards double arrow 2a = 250 rightwards double arrow a = Rs. 125
∴  Value of the certificates purchased by him in the first year = Rs. 125 New line Value of the certificates purchased by him in the 13th year = a + (13 - 1)d = 125 + 12(25) = Rs. 425

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