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Question
In the following expansion, find the indicated term.
`(3"a" + 4/"a")^13`, 10th term
Solution
We know that the (r + 1)th term in the expansion of (p + q)n is
tr+1 = nCr pn–r qr
Here p = 3a, q = `4/"a"`, n = 13 and for t10, r = 9.
∴ 10th term in the expansion of `(3"a" + 4/"a")^13`
= t10 = `""^13"C"_9 (3"a")^(13-9).(4/"a")^9`
= `""^13"C"_4 (3"a")^4.(4/"a")^9` ...[∵ nCr = nCn–r]
= `(13 xx 12 xx 11 xx 10)/(1 xx 2 xx 3 xx 4) xx 81"a"^4 xx 4^9/"a"^9`
= `715 xx 81 xx 262144 xx 1/"a"^5`
= `15182069760/"a"^5`
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