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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?

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? Correct Answer 413

Given:

The first term = 10

The fourth terms = 19

Total number of terms = 14

Formula Used:

Tn = a + (n – 1) × d

S = (n/2) ×

Where, a → First term

n → Number of terms

d → Common difference

S → The required sum

Tn → nth term

Calculation:

Tn = a + (n – 1) × d

⇒ 19 = 10 + (4 – 1) × d

⇒ 19 – 10 = 3 × d

⇒ d = 9/3

⇒ d = 3

S = (n/2) ×

⇒ (14/2) ×

⇒ 7 ×

⇒ 7 × (20 + 39)

⇒ 7 × 59

⇒ 413

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

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