Question

If $b^2,a^2,c^2$ are in A.P. then $a+c,b+c,c+a$ will be in :

• A. $A.P.$
• B. $G.P.$
• C. $H.P.$
• D. None of these

Answer 1

Answer: (A)

$A.P.$

$b^2,a^2.c^2$ are in AP

therefore

$\frac{b^2+c^2}{2}=a^2$

$b^2+c^2=2a^2$

now

$\frac{a+c+c+a}{2}=b+c$

$2a+2c=2b+2c$

$a=b$

$a+c,b+c,c+a$ are in AP