Question

find a,a,c such that the following number are in A.P:a,7,b,23,c

Answer 1

b-7=23-b (common difference )
b=15
now b-7=d (common
difference )
15-7=8=d
a2-a1=d
7-a=8
a=-1
and c =23+8
c=31

Answer 2

a, 7,b,23,c are in AP
in which,
first term (A)=a
(A2)=7
(A3)=b
(A4)=23
(A5)=c
common difference=d
A2=A+d
A4=A+3d
A4-A2=23-7
(A+3d)-(A+d)=16
A+3d-A-d=16
2d=16
d=8
A2=A+d
7=A+8
A=-1 or a=-1
A3=A+2d=-1+2×8=-1+16=15
b=15
A5=A+4d=-1+4×8=-1+32=31
c=31
so, a=-1, b=15, c=31.