Class 11

Math

Algebra

Sequences and Series

Prove that the sum of the n arithmetic means inserted between two quantities is n times the single arithmetic mean between them.

Now $x_{1}+x_{2}+x_{3}+...+x_{n}$.

$=2n (x_{1}+x_{n})=2n (T_{2}+T_{n+1})$

$=2n (a+d+b−d)=n(2a+b )$

$=$n (sngle A.M. of a and b).