Question

I have a problem solving the question below could someone help me solve it or at least give me a hint on how to solve it ? If you can help here is the question ; p,q,r are three consecutive terms of an A.P whose sum is 21. The ratio p:r = 6:1 , Find p:q:r.

Answer 1

p = x
q = x + d
r = x + 2d

x/(x+2d) = 6/1

3 x + 3 d = 21
so
x + d = 7
and
x = 6x + 12 d or 5 x = -12 d

5 x + 12 d = 0
5 x + 5 d = 35
-----------------
7 d = -35
d = -5
x = 12
etc