Question

find the value of a,b,c such tht yhe number a,7,b,23 and c are in AP

Answer 1

a , 7, b , 23 , c are in AP
so, common difference must be constant .
e.g.,
(7 - a) = (b - 7 ) = (23 - b) = (c - 23 )

now,
(7 - a ) = (b - 7)
7 + 7 = b + a
14 = a + b => a + b = 14 --------(1)

again,
(7 - a) = (23 - b)
7 - 23 = a - b
-16 = a - b --------(2)

solve equations (1) and (2)
2a = -2 => a = -1 and b = 15

now,
(c - 23) = (23 - b)
c - 23 = 23 - 15 = 8
c = 23 + 8 = 31

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

hence, series is -1, 7, 15 , 23 , 31