JEE MAIN - Mathematics (2022 - 26th July Evening Shift - No. 19)
Different A.P.'s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.'s having at least 3 terms and at most 33 terms is ___________.
Answer
53
Explanation
$${d_1} = {{199 - 100} \over 2} \notin I$$
$${d_2} = {{199 - 100} \over 3} = 33$$
$${d_3} = {{199 - 100} \over 4} \notin I$$
$${d_n} = {{199 - 100} \over {i + 1}} \in I$$
$${d_i} = 33 + 11,\,9$$
Sum of CD's $$ = 33 + 11 + 9$$
$$ = 53$$
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