Question

Find $a+b+c$ such that the following numbers are in AP: a, 7, b, 23, c.

Answer 1

Since $a,7,b,23,c$ are in AP.

$\therefore 7-a=b-7=23-b=c-23$ ....(1)

On taking $2^{nd}$ and $3^{rd}$ expression, we get,

$b-7=23-b$

$\Rightarrow 2b=30\Rightarrow b=15$

On taking $1^{st}$ and $2^{nd}$ expression, we get,

$7-a=b-7$

$\Rightarrow 7-a=15-7\Rightarrow a=-1$

Again, on taking $3^{rd}$ and $4^{th}$ expression, we get,

$23-b=c-23$

$\Rightarrow 23-15=c-23\Rightarrow c=31$

Hence $a=-1,b=15,c=31$

$\therefore a+b+c=-1+15+31=45$