Question

arithmetic mean of first 15 odd number ​

Answer 1

Answer:

15

Step-by-step explanation:

fifteen odd numbers=( 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29)

arithmetic mean= Sum of numbers/ no.of terms

= 225/15

A.Mean= 15

Answer 2

Given,

First 15 odd numbers.

To find,

Their arithmetic mean.

Solution,

The arithmetic mean also called the arithmetic average is simply the sum of values divided by the number of values. Mathematically,

$AM=\frac{sum\hspace{3} of\hspace{3} values}{number\hspace{3} of \hspace{3}values}$

Here, it is required to find the arithmetic mean of the first 15 odd numbers. So, these numbers are

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29.

It can be seen that it is an A. P. with

a = 1, d = 2, n = 15.

So, we can find the sum using the formula for the sum of an A. P. as follows.

$S_n=\frac{n}{2} [2a+(n-1)d]$

⇒ $S_n=\frac{15}{2} [2(1)+(15-1)\cdot2]$

⇒ $S_n=\frac{15}{2} [2+(14)\cdot2]$

⇒ $S_n=\frac{15}{2}\times30$

⇒ $S_n=225$

As the number of terms = 15, and the sum of the terms = 225. So, the arithmetic mean will be,

$AM=\frac{225}{15} =15$

Therefore, the arithmetic mean of the first 15 odd numbers will be 15.