Question

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

Answer 1

Let the common difference be d.

Given a1 = a

           a2 = > a + d = 7   --- (1)

           a3 = > a + 2d = b   --- (2)

           a4 = > a + 3d = 23  --- (3)

           a5 = > a + 4d = c  ---- (4)


On solving (1) and (3), we get

2d = 16

d = 8.

substitute d = 8 in any on the  above equations, we get a = -1.


substitute a = -1 in (2) we get b = -1 + 2(8)

                                                b  = 15.


substitute b = 15 in (4), we get c = -1 + 4(8)

                                                   c = 31.


The values of a = -1, b = 15, c = 31

Answer 2

Plz refer to this attachment