# 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 vote
13 views
in Aptitude
closed
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

+1 vote
by (48.2k points)
selected

Correct Answer - Option 1 : 48450

Given:

T4 = 37

T17 = 89

Formula used:

Tn = a + (n – 1) d

Sn = 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

∴ Sn = 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 × 

∴ S150 = 48450