Correct Answer - Option 1 : 48450

**Given:**

T_{4} = 37

T_{17 }= 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:**

T_{4} = 25 = a + (4 – 1) d

⇒ a + 3d = 37 ---- (1)

T_{17 }= 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]

⇒ S_{150} = 150/2 × [(2 × 25) + (150 – 1) × 4]

⇒ S_{150 }= 75 × [50 + (149 × 4)]

⇒ S_{150 }= 75 × [50 + 596]

⇒ S_{150 }= 75 × [646]

∴ S_{150} = 48450