Correct Answer - Option 2 : 1225
Given:
Average of certain first natural numbers is 25
Formula used:
Average = Sum of observations/ number of observations
Average of ‘first’ “n” natural numbers = [n + 1]/2 [When n is odd]
Average of 'first "n" natural numbers = Average of two middle terms = [(n/2)th term + (n/2 + 1)th term] / 2 [Where n is even]
Calculation:
Taking n as even will give the terms in decimal. [n is number of terms]
Hence we have to consider n as add
Average of certain first natural numbers = 25 = [n + 1]/2
⇒ n + 1 = 50
⇒ n = 49
Sum of these first 25 natural numbers = average × number of observations = 49 × 25 = 1225
∴ Sum is 1225
