# Find the middle term in the expansion of (xa-ax)10 - Mathematics and Statistics

Sum

Find the middle term in the expansion of (x/"a" - "a"/x)^10

#### Solution

Here, a = x/"a", b = -"a"/x, n = 10

Now, n is even

∴ ("n"+2)/2=(10+2)/2 = 6

∴ Middle term is t6, for which r = 5.

We have, tr+1 = nCr an−r .br

t6 = ""^10"C"_5.(x/"a")^5.(-"a"/x)^5

= 10C5 × −1

= (-10!)/(5!5!)=-(10xx9xx8xx7xx6)/(5xx4xx3xx2xx1)

= − 252

∴ Middle term is − 252.

Concept: Middle term(s) in the expansion of (a + b)n
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Methods of Induction and Binomial Theorem
Exercise 4.3 | Q 4. (iv) | Page 80