Correct Answer - Option 2 : 9
Calculation:
⇒ For 3n terms, n = 3n, a = 3, and d = a2 - a1 = 7 - 3 = 4
⇒ (3n/2) × [2 × 3 + (3n - 1) × 4]
⇒ 6n2 + n - 610 = 0
By solving this quadratic equation
⇒ n = 10, and n = -(61/6), n can not be negative we will consider n = 10
⇒ for positive integer m
⇒ m × (3 + 7 + 11 + ............. + 39) > 1830
⇒ m × (10/2) × [2 × 3 + (10 - 1) × 4] > 1830
By solving
⇒ m > 8.71 ≈ 9
∴ The required result will be 9.
Sn = (n/2) × [2a + (n - 1) × d]
Where a = First term, n = Number of term, d = difference