Question

Arithmetic mean of series a+(a+d)+(a+d)+(a+2d)......(a+2nd)is

Answer 1

hello...

The given Series is a, a+d, a+2d, a+3d, ... a+2nd.......

 its first term=a

 common difference=d

mth term=a+2nd

let no. of terms =m

So, am=a+(m-1)d
⇒a+2nd=a+(m-1)d
⇒2nd=(m-1)d
⇒2n=(m-1)
⇒m=2n+1....

Sm=m2(a+am)
⇒Sm=2n+12(a+a+2nd)
⇒Sm=2n+12(2a+2nd)
⇒Sm=2n+122(a+nd)
⇒Sm=(2n+1)(a+nd)..


so  Arithmetic Mean
=Sm
m=(2n+1)(a+nd)(2n+1)=a+nd


Arithmetic Mean of the Series is a+nd.



thank you
 

Answer 2

The answer is ...

a+nd

By doing arithmetic progession we get the answer