CAT 2003 Slot 1 — QA Question 10
Miscellaneous ProgressionsEasy
The sum of 3rd and 15th elements of an arithmetic progression is equal to the sum of 6th, 11th and 13th elements of the same progression. Then which element of the series should necessarily be equal to zero?
Answer & solution
Correct answer: 12th
- A
1st
- B
9th
12th
- D
None of the above
Solution
Assume that the first term of the progression is a and the common difference is d.
âµ T3 + T15 = T6 + T11 + T13
∴ (a + 2d) + (a + 14d) = (a + 5d) + (a + 10d) + (a + 12d)
∴ a + 11d = 0
But, T12 = a + 11d
∴ The 12th term of an arithmetic progression is 0.
Hence, option (c).