Advertisement Remove all ads

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

Sum

Answer the following:

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

Advertisement Remove all ads

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
  Is there an error in this question or solution?
Advertisement Remove all ads

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
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×