Sample Problems on General Term
Example 1: Find (r+1)th term for the given binomial expansion (x + 2y)5
Solution:
Given expansion is (x + 2y)5
a = x, b= 2y, n = 5
The formula for (r+1)th is nCr .an – r.br
(r+1)th term =5Cr.x5 -r.2yr
Example 2: Find (r+1)th term for the given binomial expansion (a + 2b)7
Solution:
Given expansion is (a + 2b)7
a = a, b = 2b, n = 7
The formula for (r+1)th is nCr .an – r.br
(r+1)th term = 7Cr.a7 -r.br
Example 3: Find (r + 1)th term for the given binomial expansion (6p + 2q)12
Solution:
Given expansion is (6p + 2q)
a = 6p, b = 2q, n = 12
The formula for (r+1)th is nCr .an – r.br
(r + 1)th term = 12Cr.6p12 -r.2qr
General and Middle Terms – Binomial Theorem – Class 11 Maths
Binomial theorem or expansion describes the algebraic expansion of powers of a binomial. According to this theorem, it is possible to expand the polynomial “(a + b)n“ into a sum involving terms of the form “axzyc“, the exponents z and c are non-negative integers where z + c = n, and the coefficient of each term is a positive integer depending on the values of n and b.
Example: If n = 4
(a + b)4 = a4 + 4a3y + 6a2b2 + 4ab3 + b
Table of Content
- General Term of Binomial Expansion
- Sample Problems on General Term
- Middle Term of Binomial Expansion
- Sample Problems on Middle Terms
- Examples on Middle Terms
- FAQs on General Term and Middle Term