Progression arithmetic/geometric

I tried to equate the system but could not find the solution. Could anyone help?

The sequence $(a_1, a_2, a_3, \ldots)$ is an arithmetic progression with common difference $3$, and the sequence $(b_1, b_2, b_3, \ldots)$ is an increasing geometric progression. Knowing that $a_2 = b_3$, $a_{10} = b_5$ and $a_{42} = b_7$, the value of $b_4-a_4$ is:

Given Options

• a. 2




• b. 0




• c. 1




• d. -1