Question

Find a,b and c such that a,7,b,23,c are ap

Answer 1

7-a=b-7
a+b=14 ( 1)  similarly a+c=30 (2)
substitute 1 in 2
c-b=16
b+c=46
2c=62
c=31
d=31-23=8 so b=15
and a=-1
 there are other complex methods but this is easier to understand 

Answer 2

7-a=b-7=23-b=c-23
on equating, b-7=23-b
2b=30
b=15
on equating, 7-a=b-7
7-a=8
a=-1
on equating, 23-b=c-23
c=46-15
c=31