Correct Answer - Option 4 : -930

**Given:**

a = -2,

S_{15} = 24/65 × S_{25}

**Formula used:**

S_{n} = n/2 × [2a + (n – 1) d]

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

**Calculation:**

S_{15} = 15/2 × [2(-2) + (15 – 1) d]

⇒ S_{15} = 15/2 × (- 4 + 14d)

⇒ S_{15} = (-30 + 105d) ---- (1)

S_{25} = 25/2 × [2(-2) + (25 – 1) d]

⇒ S_{25} = 25/2 × (-4 + 24d)

⇒ S_{25} = (-50 + 300d) ----- (2)

According to question –

⇒ S_{15} = 24/65 × S_{25}

⇒ -30 + 105d = 24/65 × (-50 + 300d)

⇒ -1950 + 6825d = -1200 + 7200d

⇒ (7200 – 6825) d = (-1950 + 1200)

⇒ 375d = -750

d = -2

Now, S_{30} = 30/2 × [2(-2) + (30 – 1) × (-2) ]

⇒ S_{30 }= 15[- 4 - 58]

⇒ S_{30} = 15 × (-62)

∴ S_{30} = - 930