Class 11

Math

Algebra

Sequences and Series

Find $x$, if the given numbers are in A.P. $(a+b)_{2},x,(a−b)_{2}$

Here, it is given that $AM=x$, $a=(a+b)_{2}$ and $b=(a−b)_{2}$, therefore,

$AM=2a+b ⇒x=2(a+b)_{2}+(a−b)_{2} ⇒x=2(a_{2}+b_{2}+2ab)+(a_{2}+b_{2}−2ab) ⇒x=22a_{2}+2b_{2} ⇒x=22(a_{2}+b_{2}) ⇒x=a_{2}+b_{2}$

Hence, $x=a_{2}+b_{2}$