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The sum of the 6th and 15th elements of an arithmetic progression is equal to the sum of 7th, 10th and 12th elements of the same progression. Which element of the series should necessarily be equal to zero ?
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- 10th
- 8th
- 1st
- 9th
- 10th
Correct Option: B
Let the first term and common term of the AP be a and d respectively.
Then, According to question ,
Sum of 6th and 15th elements = Sum of 7th, 10th and 12th elements
(a + 5d) + (a + 14d) = (a + 6d) + (a + 9d) + (a + 11d)
⇒ 2a + 19d = 3a + 26 d
⇒ a + 7d = 0
∴ 8th term is 0.
