Correct Answer - Option 4 : 30
Given,
An arithmetic series, (25 + 50 + 75 + 100 + 125......)
Formula used:
Sum of n terms of an A.P. = (n/2) × {2a + (n - 1)D}
Calculation:
∵ Given series (25 + 50 + 75 + 100 + 125......) is an A.P.
a = 25, D = 25, sum = 11625
If n terms of the series are taken to give a sum of 11625
⇒ 11625 = (n/2) × {2 × 25 + (n - 1) × 25}
⇒ 11625 = (n/2) × {50 + 25 n - 25}
⇒ 11625 = (n/2) × {25 + 25 n}
⇒ 11625/25 = (n/2) × (n + 1)
⇒ 465× 2 = n2 + n ---- (i)
⇒ n2 + n – 930 = 0
⇒ n2+ 31 n – 30 n – 930 = 0
⇒ n(n + 31) -30(n - 31) =0
⇒ (n + 31) (n - 30) = 0
⇒ n= 30, -31
⇒ n = 30
∴ Required number of terms are 30
Or we can calculate the equation (i) like this
465× 2 = n2 + n
⇒ 930 = n(n + 1)
⇒ 30 × 31 = n × (n + 1)
⇒ n = 30
∴ Required number of terms are 30
