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  • If the 6th term in the expansion of <img alt="(\frac{3}{2} + \frac{x}{2})^{n}" src="https://entrancecorner.oncodecogs.com/gif.latex?%28%5Cfrac%7B3%7D%7B2%7D%20&plus;%20%5Cfrac%7

If the 6th term in the expansion of (\frac{3}{2} + \frac{x}{2})^{n}is numerically greatest, when x = 2, then the sum of possible integral values of 'n' is:

Option: 1

23


Option: 2

24


Option: 3

25


Option: 4

26


Answers (1)

best_answer

For T6 to be numerically the greatest term, T6 > T5

\implies ^{n}C_{5}(\frac{3}{2})^{n-5} > ^{n}C_{4}(\frac{3}{2})^{n-4}

\implies 2n > 23                    \implies n > 11.5

Also T6 > T7         \implies ^{n}C_{5}(\frac{3}{2})^{n-5} > ^{n}C_{6}(\frac{3}{2})^{n-6}

\implies n - 5 < 9            \implies n < 14

From (i) & (ii), we get n = 12, 13

Required sum = 12 + 13 = 25

Posted by

Ritika Kankaria

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