SOLUTION: Hi, im finding difficulty trying to answer these two questions, help would be much appreciated, thank you very much. (a)Find a and b if a,1,a+b forms a geometric progression and

Algebra ->  College  -> Linear Algebra -> SOLUTION: Hi, im finding difficulty trying to answer these two questions, help would be much appreciated, thank you very much. (a)Find a and b if a,1,a+b forms a geometric progression and      Log On


   

Question 973410: Hi, im finding difficulty trying to answer these two questions, help would be much appreciated, thank you very much.
(a)Find a and b if a,1,a+b forms a geometric progression and b,1/2,a-b forms an arithmetic progression
(b)Show that if the first, second and fourth terms of an arithmetic progression form a geometric sequence, then either the sequence is a constant sequence, or the terms are the positive integer multiples of the first term.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
(b):
First four terms, a, a+d, a+2d, a+4d

This arrangement is geometric progression: a, a%2Bd, a%2B4d;
Let r be the common ratio.
%28a%2Bd%29%2Fa=r, %28a%2B4d%29%2F%28a%2Bd%29=r, %28a%2B4d%29%2Fa=r%5E2

Try forming equations from those ratio related relationships.
highlight%28%28a%2Bd%29%2Fa=%28a%2B4d%29%2F%28a%2Bd%29%29 and highlight%28%28%28a%2B4d%29%2F%28a%2Bd%29%29%5E2=%28a%2B4d%29%2Fa%29

What happens if solve these last two equations for a and d?
That is the strategy to try, but I have not yet done further.