Correct Answer - Option 4 : -930
Given:
a = -2,
S15 = 24/65 × S25
Formula used:
Sn = n/2 × [2a + (n – 1) d]
Where, a = first term, n = number of terms and d = common difference
Calculation:
S15 = 15/2 × [2(-2) + (15 – 1) d]
⇒ S15 = 15/2 × (- 4 + 14d)
⇒ S15 = (-30 + 105d) ---- (1)
S25 = 25/2 × [2(-2) + (25 – 1) d]
⇒ S25 = 25/2 × (-4 + 24d)
⇒ S25 = (-50 + 300d) ----- (2)
According to question –
⇒ S15 = 24/65 × S25
⇒ -30 + 105d = 24/65 × (-50 + 300d)
⇒ -1950 + 6825d = -1200 + 7200d
⇒ (7200 – 6825) d = (-1950 + 1200)
⇒ 375d = -750
d = -2
Now, S30 = 30/2 × [2(-2) + (30 – 1) × (-2) ]
⇒ S30 = 15[- 4 - 58]
⇒ S30 = 15 × (-62)
∴ S30 = - 930