Question

The term-to term of the sequence is

Answer 1

It is given that the third terms is obtained by multiplying the second term by 2 and then adding 3:

$a_3 = 2a_2+3$

Since the third term is 17, we have

$17=2a_2+3 \iff 2a_2=14\iff a_2=7$

And then again, the second term is obtained by multiplying the first one by 2 and then adding three:

$a_2 = 7 = 2a_1+3$

Solve this equation for $a_1$ and you'll get the answer