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Question

If 6 times the 6th term of an AP is equal to 21 times the 21st term of that AP, then 27th term of the same AP is ___
  1. 1
  2. 0
  3. -1
  4. -2


Solution

The correct option is B 0
Given,
6a6=21a21
  6[a + (6 - 1)d] = 21[a + (21 - 1)d]
   6(a + 5d) = 21(a + 20d)
    6a + 30d = 21a + 420d
    -15a - 390d = 0
     15a + 390d = 0
    a + 26d = 0
     a + (27 - 1)d = 0
Hence, 27th term of the same AP is 0.

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