Question

Find a , b c such that the following numbers are in AP a,7,b,23,c

Answer 1

a, 7 , b , 23 , c are in AP

so, 7 - a = b - 7 = 23 - b = c -23

-b - a = -14
a + b = 14 --------(1)

2b = 30
b = 15
put this in equation (1)

a = -1

now , again ,

b + c = 46
c = 46 -15 = 31

Answer 2

a,7,b,23,c are in AP
let the common difference = d
b-7 = d----(1)
23-b = d---(2)
add (1) and (2)

16 = 2d
2d = 16
∴d=16/2= 8
i) d= 7-a
8=7-a⇒8-7 =-a


1= -a
∴a= -1
ii) b-7=d
b-7=8
b=8+7
b=15
iii)c-23=d
c-23=8
c=8+23
c=31
∴a =-1, b=15, c=31