No
Yes, for all values of
$a$
Yes, but only for certain values of
$a$

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

I think an easier solution is to treat the first three terms of an AP as if they are a GP:

$\displaystyle \begin{aligned} \frac{a+d}{a} &= \frac{a+2d}{a+d} \\ \therefore (a+d)^2 &= a(a+2d) \end{aligned}$

Simplifying this gives $d^2 = 0 \Rightarrow d = 0$ , which is not positive.

Therefore there is no solution.