The last term in the expansion of 2 1 3 + 2 - 1 2 n is 3 - 5 3 l o g 3 8 . Then, the value of the fifth term is

Question

The last term in the expansion of 2 1 3 + 2 - 1 2 n is 3 - 5 3 l o g 3 8 . Then, the value of the fifth term is, 110, 210, 310, 220

MARKS App · Accepted Answer

We are given that last terms is 3 - 5 3 l o g 3 8 = 3 - 5 3 3 l o g 3 2 3 l o g 3 2 - 5 = 2 - 5 = 1 32 Also, last term is n C n 2 - 1 2 n = 2 - n 2 ⇒ 2 - 5 = 2 - n 2 ⇒ n = 10 The fifth term is 10 C 4 2 1 3 6 2 - 1 2 4 = 10 × 9 × 8 × 7 4 × 3 × 2 × 2 2 × 2 - 2 = 210

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