Question

In a certain sequence of numbers, each term after the first is found by doubling and then adding $3$ to the previous term. If the seventh term of the sequence is $125$, what is the first term?

Answer 1

Given $a_7=125$ you can find a_6:

$a_6= \frac{125-3}{2} =61$
 $a_5= \frac{61-3}{2} =29 \\ a_4= \frac{29-3}{2}=13 \\ a_3= \frac{13-3}{2} =5 \\ a_2= \frac{5-3}{2} =1 \\ a_1= \frac{1-3}{2}=-1$
Answer: -1