Question

The nth term of an AP is 7-4nFind its common difference and sum of n terms ​

Answer 1

Given:- nₜₕ term of an AP is 7 -4n

Solution :-

As given that, aₙ = 7 - 4n ...eq(1)

• Let's put n = 1 in eq(1)

a₁ = 7 - 4(1)

a₁ = 3

• Now, put n = 2 in eq(2)

a₂ = 7 - 4(2)

a₂ = 7 - 8

a₂ = -1

Common difference(d) = a₂ - a₁

d = -1 - 3

d = -4

Hence, the common difference is -4.

⇒ Sum of nₜₕ terms:-

Sₙ = n/2 [2a + (n-1)d]

Sₙ = n/2 [ 2(3) + (n-1)-4]

Sₙ = n/2 (6 - 4n +4)

Sₙ = n/2 × 2(3-2n+2)

Sₙ = n (3-2n+2)

Sₙ = 3n - 2n² + 2n

Hence, the sum of nₜₕ term is 3n-2n²+2n.

Answer 2

Given:- nₜₕ term of an AP is 7 -4n

Solution :-

As given that, aₙ = 7 - 4n ...eq(1)

• Let's put n = 1 in eq(1)

a₁ = 7 - 4(1)

a₁ = 3

• Now, put n = 2 in eq(2)

a₂ = 7 - 4(2)

a₂ = 7 - 8

a₂ = -1

Common difference(d) = a₂ - a₁

d = -1 - 3

d = -4

Hence, the common difference is -4.

⇒ Sum of nₜₕ terms:-

Sₙ = n/2 [2a + (n-1)d]

Sₙ = n/2 [ 2(3) + (n-1)-4]

Sₙ = n/2 (6 - 4n +4)

Sₙ = n/2 × 2(3-2n+2)

Sₙ = n (3-2n+2)

Sₙ = 3n - 2n² + 2n

Hence, the sum of nₜₕ term is 3n-2n²+2n.