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  ⁿC_r .a^{n – r}.b^r

(r+1)^th term =⁵C_r.x^{5 -r}.2y^r

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  ⁿC_r .a^{n – r}.b^r

(r+1)^th term = ⁷C_r.a^{7 -r}.b^r

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  ⁿC_r .a^{n – r}.b^r

(r + 1)^th term = ¹²C_r.6p^{12 -r}.2q^r

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 “ax^zy^c“, 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