Question

Find the sum of the first 150 terms of an arithmetic sequence given that the fourth term is 37 and the seventeen term is 89.
1. 48450
2. 45850
3. 44950
4. 46850

Answer 1

Correct Answer - Option 1 : 48450

Given:

T₄ = 37

T₁₇ = 89

Formula used:

T_n = a + (n – 1) d

S_n = n/2 × [2a + (n – 1) d]

Where, a = first term, n = number of terms, d = common difference

Calculation:

T₄ = 25 = a + (4 – 1) d

⇒ a + 3d = 37      ---- (1)

T₁₇ = 89 = a + (17 – 1) d

⇒ a + 16d = 89      ---- (2)

Subtract equation (1) from (2), we have –

⇒ a + 16d – a – 3d = 89 – 37

⇒ 13d = 52

⇒ d = 52/13

⇒ d = 4

Substitute the value of d in equation (1), we have –

⇒ a + 3(4) = 37

⇒ a = 37 – 12

⇒ a = 25

∴ S_n = n/2 × [2a + (n – 1) d]

⇒ S₁₅₀ = 150/2 × [(2 × 25) + (150 – 1) × 4]

⇒ S₁₅₀ = 75 × [50 + (149 × 4)]

⇒ S₁₅₀ = 75 × [50 + 596]

⇒ S₁₅₀ = 75 × [646]

∴ S₁₅₀ = 48450