Correct Answer - Option 2 : 20
Given:
Average of certain first consecutive natural numbers is 10.5
Formula used:
Average = Sum of observations / Number of observations
Average of ‘first’ “n” natural numbers = [(n + 1)/2]th term [When number of terms are odd]
Average of ‘first’ “n” natural numbers = Average of the two middle terms = [(n/2)th term + (n/2 + 1)th term] / 2 [When number of terms are even]
Calculation:
As the terms are consecutive so the middle term cannot be 10.5 as they are natural numbers hence the number of terms are even.
Let the middle terms be x and x + 1
⇒ Average of middle terms = (2x + 1)/2
⇒ (2x + 1)/2 = 10.5
⇒ x = 20/2 = 10
Middle terns are 10 and 11
There are 9 terms before 10, so there will be 9 terms after 11
Hence number of terms = 11 + 9 = 20
∴ Number of certain first consecutive natural numbers whose average is 10.5 is 20
