The sum of 3rd and 15th elements of an arithmetic progression is equal to the sum of the 6th, 11th and 13th elements of the same progression. Then, which element of the series should necessarily be equal to zero ?
Correct answer: C
Explanation
Let the 1st term be ‘a’ and common difference be ‘d’
then we have 3rd term = a + 2d
15th term = a + 14d
6th term = a + 5d
11th term = a + 10d
13th term = a + 12d
Since sum of 3rd and 15th term = sum of 6th, 11th and 13th term, therefore we have
=> 2a + 16d = 3a + 27d
=> a + 11d = 0 i.e the 12th term.
C
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AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.