Question 61

What is the average of first 15 whole numbers?

Solution

The first 15 whole numbers are 0,1,2,3,......14.

Average formula = $$\frac{sum\ of\ all\ terms\ in\ the\ given\ series}{number\ of\ terms\ present\ in\ the\ series}$$

So,for finding average of these above numbers we should add all the numbers and divide it by 15.

As,we can see here that this series of whole numbers is in AP. So, here we can use directly the AP series formula which is as follow for n terms,

S$$_{n} $$= $$\frac{n}{2}$$ $$ \times$$({2}{a}+(n-1)$$\times$${d}$$ $$)

So for 15 terms ,here,n=15,a=0,d=1, where 'a' and 'd' are first term and common difference in AP series respectively.

After putting in the above formula we get;

S$$_{15}$$=$$\frac{15}{2}$$ $$\times$$({2}{0}+(15-1)$$\times$${1}$$ $$)

S$$_{15}$$= $$\frac{15}{2}$$ $$\times$${14}$$  $$    

         ={15}$$\times$${7}$$ $$

So, the average of first 15 whole numbers is 7.


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