Question

The nth term of an AP is 7 - 4n. Find the sum of first n terms of the AP.

quickly pls s
it's very urgent​

Answer 1

Answer- The above question is from the chapter 'Arithmetic Progressions'.

Concept used: 1) aₙ = nth term

2) a₂ - a₁ = a₃ - a₂ = d (Common difference)

3) Sₙ = $\frac{n}{2} [2a \: + (n-1)d]$

Given question: The nth term of an AP is 7 - 4n. Find the sum of first n terms of the AP.

Answer: aₙ = 7 - 4n

Put n = 1, 2, 3, _ _ _

a₁ = 7 - 4(1) = 7 - 4 = 3

a₂ = 7 - 4(2) = 7 - 8 = -1

a₃ = 7 - 4(3) = 7 - 12 = -5

d = a₂ - a₁  = - 1 - 3 = - 4

No. of terms = n

Sₙ = $\frac{n}{2} [2a \: + (n-1)d]$

Sₙ = $\frac{n}{2} [2*3 + (n-1)-4]$

Sₙ = $\frac{n}{2} (6 - 4n + 4)$

Sₙ = $\frac{n}{2} \times 2(5 - 2n)$

Sₙ = n (5 - 2n)

Sₙ = 5n - 2n²

∴ Required sum of first n terms of the AP = 5n - 2n².