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If Sn denotes the sum of …

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If Sn denotes the sum of first nth terms of an AP. Prove that S12=3(S8-S4).
  • 1 answers

Saksham Hinge 3 months ago

Let 1 s t term of A . P = a and common difference = d We have to prove that S 12 = 3 ( S 8 − S 4 ) S 12 = 12 2 [ 2 a + ( 12 − 1 ) d ] S 8 = 8 2 [ 2 a + ( 8 − 1 ) d ] S 4 = 4 2 [ 2 a + ( 4 − 1 ) d ] Now, R . H . S = 3 ( S 8 − S 4 ) = 3 [ 8 2 ( 2 a + ( 8 − 1 ) d − 4 2 ( 2 a + ( 4 − 1 ) d ] = 3 [ 8 x + 28 d − 4 a − 6 d ] = 6 ( 2 a + 11 d ) = 12 2 [ 2 a + ( 12 − 1 ) d ] = S 12 = L . H . S
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