# Answer the following: Find the middle term (s) in the expansion of (2a3-32a)6 - Mathematics and Statistics

Sum

Find the middle term (s) in the expansion of ((2"a")/3 - 3/(2"a"))^6

#### Solution

Here a = (2"a")/3, b = (-3)/(2"a"), n = 6

Since n is even

∴  ("n" + 2)/2 = (6 + 2)/2 = 4

∴ Middle term is t4, for which r = 3

We have tr+1 = nCr an–r.br

∴ t4 = ""^6"C"_3 ((2"a")/3)^3 ((-3)/(2"a"))^3

= (6!)/(3!3!) xx (-1)

= (-6 xx 5 xx 4 xx 3)/(3 xx 2 xx 1 xx 3!)

= – 20

∴  Middle term is – 20.

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
Miscellaneous Exercise 4 | Q II. (8) (i) | Page 85