Question

There is an A.P. whose first term is 10, and the fourth term is 19. What will be the sum of the first 14 terms?
1. 413
2. 393
3. 313
4. 400

Answer 1

Correct Answer - Option 1 : 413

Given:

The first term = 10

The fourth terms = 19

Total number of terms = 14

Formula Used:

T_n = a + (n – 1) × d

S = (n/2) × [2 × a + (n – 1) × d]

Where, a → First term

n → Number of terms

d → Common difference

S → The required sum

T_n → n^th term

Calculation:

T_n = a + (n – 1) × d

⇒ 19 = 10 + (4 – 1) × d

⇒ 19 – 10 = 3 × d

⇒ d = 9/3

⇒ d = 3

S = (n/2) × [2 × a + (n – 1) × d]

⇒ (14/2) × [2 × 10 + (14 – 1) × 3]

⇒ 7 × [20 + 13 × 3]

⇒ 7 × (20 + 39)

⇒ 7 × 59

⇒ 413

∴ The sum of first 14 terms of A.P. is 413.