Question

The sixth term of an AP is 22 and the 10th term is 34. Find the sum to the first 16 terms of the AP.

Answer 1

Answer:

S₁₆ = 472

Step-by-step explanation:

Given:

t₆ = a + 5d = 22

t₁₀ = a + 9d = 34

Required:

To find the sum of First 16 terms

Equation used:

ⁿ/₂(t₁ + t₁₆)

Solution:

a + 5d = 22-----(1)

a + 9d = 34-----(2)

      -4d = -12

      d = 3

Put 'd' in Eqn (1) / (2)

a + 5 × 3 = 22

a + 15 = 22

a = 22 - 15 = 7

t₁₆ = a + 15d

t₁₆ = 7 + 15 × 3

t₁₆ = 7 + 45

t₁₆ = 52

S₁₆ = ⁿ/₂(t₁ + t₁₆)

S₁₆ = ¹⁶/₂(7 + 52)

S₁₆ = ¹⁶/₂(59)

S₁₆ = 472