Find the values of A and Q in the AP _ 12,P,Q ,18

Answer 1

If your question means:

Find the values of A and Q in the AP - 12,P,Q ,18

then

In an Arithmetic Progression:

an = a1 + ( n - 1 ) d

where

a1 = the initial term

d = the common difference of successive members

an = the nth term

In this case:

a1 = - 12

a4 = a1 + 3 d

18 = - 12 + 3 d

Add 12 to both sides

30 = 3 d

d = 30 / 3 = 10

P = a2 = a1 + d = - 12 + 10 = - 2

Q = a3 = a1 + 2 d = - 12 + 2 ∙ 10 = - 12 + 20 = 8

Answer 2

3d = 18-12
so d = 2
...,12,14,16,18,...