Question

find the value of a,b and c such that the numbers a, 7,b,23,and c are in A.P

Answer 1

common difference, d = 7-a = c-23
a+c = 30
b = a+c\2
= 30/2
b = 15.
d = b-7
= 15-7
d = 8.
Therefore, 8 = 7-a
a = -1.
c-23 = 8
c = 8+23
c = 31.
Therefore, a = -1
b = 8
c = 31

Answer 2

given a.p. a,7,b,23,c
so common difference between them
b-7=7-a
a+b=14_____eqn1
23-b=7-a
a-b=-16
a-(14-a)=-16(by eqn 1)
a-14+a=-16
2a=-2
a=-1
putting value of a in eqn 1
we have
-1+b=14
b=15
c=23+d(common difference)
c=23+8
c=31