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AP EAMCET20224 Jul 2022Evening ShiftMathematicsDeterminantsActual

If a , b , c are respectively the 5 th , 8 th , 13 th terms of an arithmetic progression, then a 5 1 b 8 1 c 13 1 =

Options

  1. A0
  2. B1
  3. Ca b c
  4. D520

Correct answer

A. 0

Step-by-step solution

Since, a , b , c are the 5 th   , 8 th   an 13 th   term of an A . P . , respectively, therefore a = A + 4 D b = A + 7 D c = A + 12 D whew, A and D awe the first term and common differince of an A . P . . Now, a 5 1 b 8 1 c 13 1 Applying R 2 → R 2 - R 1 and R 3 → R 3 - R 1 = a 5 1 b - a 3 0 c - a 8 0 = 8 b - 8 a - 3 c + 3 a = D 56 - 32 - 36 + 12 = 0

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