Question

Find the sum of first 14 terms an AP if its first term is 10 and 20^th term is 200.

1. 1050
2. 1100
3. 1150
4. 1200

Answer 1

Correct Answer - Option 1 : 1050

CONCEPT:

• The n^th term an of the AP with first term a and common difference d is given by a_n = a + (n – 1) d.

• The sum of the first n terms of an AP is given by \(\rm S=\rm\frac{n}{2}[2a+(n-1)d]\).

CALCULATION : 

Given that : a = 10, a₂₀ = 200.

As we know that an = a + (n – 1) d.

⇒ 200 = 10 + (20 - 1) × d

⇒ d = 10

Again  \(\rm S=\rm\frac{n}{2}[2a+(n-1)d]\)

⇒ S₁₄ = 1050

Hence, option (1) is the correct answer.