Question

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

Answer 1

b-7=23-b
2b=30
b=15
7-a=23-15
a=-1
and by this method we can find c also

Answer 2

$\bf\huge\underline{Question}$⠀

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

$\bf\huge\underline{Solution}$

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

Therefore 7 - a = b - 7 = 23 - b = c - 23

Taking second and third terms, we get

⠀⠀b - 7 = 23 - b

=> 2b = 30

Therefore, b = 15

Taking first and second terms, we get

⠀⠀7 - a = b - 7

=> 7 - a = 15 - 7 ⠀⠀⠀⠀⠀⠀⠀⠀⠀[b = 15]

=> 7 - a = 8

Therefore, a = -1

Taking third and fourth terms, we get

⠀⠀23 - b = c - 23

=> 23 - 15 = c - 23⠀⠀⠀⠀⠀⠀⠀⠀[b = 15]

=> 8 = c - 23

=> 8 + 23 = c

Therefore, c = 31

⠀

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