Average Aptitude Set 7

31) Find the average of first 20 consecutive natural numbers.

12.20
10.78
16.45
10.5

Answer: D

Explanation:
The average of first n consecutive natural numbers is given by;
=(n+1)/2
Here, n=20
So, average = (20+1)/2
=210/20
=21/2
=10.5

32) Find the average of square of first 5 consecutive natural numbers.

Answer: D

Explanation:
The average of square of first n consecutive natural numbers is given by;
= (n+1) (2n+1) / 6
Here, n=5
= (5+1) (2*5+1)/6
= 6*11/6
= 11

33) Find the average of cubes of first 7 consecutive natural numbers.

Answer: A

Explanation:
The average of cubes of first n consecutive natural numbers is given by;
= n (n+1)²/4
Here, n=7
= 7 (7+1)²/4
= 7*64/4
=448/4
= 112

34) Find the average of first 8 consecutive odd numbers.

Answer: C

Explanation:
The average of first n consecutive odd numbers is equal to n, so the average of first 8 consecutive odd numbers is 8.
You can check by solving it as show below:
= (1+ 3+ 5+ 7+ 9+ 11+ 13+ 15)/8
= 64/8 = 8

35) Find the average of the square of first 5 consecutive odd numbers starting from 1 to 9, where the last odd number is 9.

Answer: D

Explanation:
The average of square of first n consecutive odd numbers starting from 1 to X, where the last odd number is X, is given by:
=X(X+2)/3
Here, X=9
So, average =9(9+2)/3
=9*11/3
=99/3
=33