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 (integer)
53
Solution
<p>${d_1} = {{199 - 100} \over 2} \notin I$</p>
<p>${d_2} = {{199 - 100} \over 3} = 33$</p>
<p>${d_3} = {{199 - 100} \over 4} \notin I$</p>
<p>${d_n} = {{199 - 100} \over {i + 1}} \in I$</p>
<p>${d_i} = 33 + 11,\,9$</p>
<p>Sum of CD's $= 33 + 11 + 9$</p>
<p>$= 53$</p>
About this question
Subject: Mathematics · Chapter: Sequences and Series · Topic: Arithmetic Progression
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