Question

the average of 1,3,5,7,9,11...25 terms is

Answer 1

The number of terms is
N = (25 - 1) / 2  + 1 = 13
The sum of terms, which is the arithmetic progression with difference 2, is:
S = (1 + 25) × 13 ÷ 2 = 13 × 13
The average is:
A = S / N = 13 × 13 / 13 = 13

So, to calculate the average of arithmetic progression was needed to calculate the number of terms N, the average arithmetic progression is the average of first and last term:
A = (1 + 25) / 2 = 13

Answer 2

The sum of the first N odd natural numbers
1+3 +...+ (2n-1)=n(1+2n-1)/2 = n^2
Here the sum of 1,3,5,7,9,11,... 25th terms is 25^2=625
i hope this will help u