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

23 views

closed

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

1. 1050
2. 1100
3. 1150
4. 1200
5. None of these

by (30.0k points)
selected

Correct Answer - Option 1 : 1050

CONCEPT:

• The nth term an of the AP with first term a and common difference d is given by an = 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.