Question

Find the values of P and Q in an Ap -12,P,Q,18

Answer 1

there are three jumps from-12 to 18, a distance of 30.Each jump 10.
-12,-2, 8,18, 28, ....

Answer 2

In an arithmetic progression;

a1

a2 = a1 + d

a3 = a1 + 2d

a4 = a1 + 3d


In this case:

a1 = -12

a2 = P

a3 = Q

a4 = 18


a4 - a1 = a1 + 3d - a1

a4 - a1 = 3 d

18 - ( - 12 ) = 3 d

18 + 12 = 3 d

30 = 3 d

3 d = 30

Divide both sides by 3

d = 10


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


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

Answer 3

T1= a (-12)
T2= a+d (p)
T3= a+2d (q)
T4= a+3d (18)
T4 - T1 = a +3d - a
T4