Ratio-Arithmetic Sequences

Call a sequence $\{a_n\}$ ratio-arithmetic with ratio-difference $t$ if

Determine, with proof, which of the following are true:

1. every geometric sequence is ratio-arithmetic, but not every arithmetic sequence is; 2. the sequence $a_n = \dfrac{2^{n-1}}{n^2}$ is ratio-arithmetic with $t = \dfrac{1}{2}$; 3. the Fibonacci-type sequence with $a_1 = 1$, $a_2 = 2$, $a_n = a_{n-1} + a_{n-2}$ ($n \geqslant 3$) is not ratio-arithmetic; 4. if $\{a_n\}$ is arithmetic and $\{b_n\}$ is geometric, then $\{a_nb_n\}$ is ratio-arithmetic.