Question 41
We have two progressions of real numbers, an arithmetic one $(a_n)_{n \in \mathbb{N}}$ and a non-constant geometric one $(g_n)_{n \in \mathbb{N}}$. It holds that $a_1 = g_1 \neq 0$, $a_2 = g_2$ and $a_{10} = g_3$. Decide, with justification, whether for every positive integer $p$ there exists a positive integer $m$ such that $g_p = a_m$.