Question

what is the arithmetic mean of the natural numbers from 10to30​

Answer 1

Answer:

mean = average

Step-by-step explanation:

10to 30 natural numbers are the numbers lieing between 10to 30

mean =. sum of observation/no. of observation

11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30/20

=20

therefore answer is 20

Answer 2

Arithmetic mean of the natural number from 10 to 30 is 20

Given:

• Natural number from 10 to 30

To Find:

• Arithmetic mean

Solution:

Natural Numbers are positive Integers

$\text{Mean}=\dfrac{\text{sum of all the obervations}}{\text{number of the observations}}$

Arithmetic sequence

Sequence of terms in which difference between one term and the next is a constant.

This is also called Arithmetic Progression AP

Arithmetic sequence can be represented in the form :

a, a + d  , a + 2d , …………………………, a + (n-1)d

a = First term

d = common difference = aₙ-aₙ₋₁

nth term =  aₙ =  a + (n-1)d

Sₙ = (n/2)(2a + (n - 1)d)

Sₙ = (n/2)( a + aₙ)

Step 1:

Natural Numbers from 10 to 30 form an AP with

a = 10  , d  = 1 , last term = 30

Step 2:

Find number of term

30 = 10 + (n - 1)1

=> 20 = n - 1

=> 21 = n

Step 3:

Find Sum of  21 terms

(21/2)(10 + 30)

= 21(20)

Step 4:

Divide by number of term 21 to find arithmetic mean

21 (20)/21

= 20

Hence, Arithmetic mean of the natural number from 10 to 30 is 20