**Question:** The 1st term of an arithmetic progression is $\displaystyle a$ and the common difference is $\displaystyle d$, where $\displaystyle d \neq 0$. (i) Write down expressions, in terms of $\displaystyle a$ and $\displaystyle d$, for the 5th term and 15th term. The 1st term, the 5th term and the 15th term of the arithmetic progression are the first terms of a geometric progression. (ii) Show that $\displaystyle 3a = 8d$. (iii) Find the common ratio of the geometric progression. **Attempt:** (i) $\displaystyle U_5 = a + 4d$

$\displaystyle U_{15} = a + 14d$

(ii) Arithmetic Progression
$\displaystyle U_5 = a + 4d$

$\displaystyle U_{15} = a + 14d$

Geometric Progression
$\displaystyle U_2 = a.r$

$\displaystyle U_3 = a.r^2$

I don't know what to do next... Need help!