Chapter 6 - Exponential Functions and Sequences - 6.7 - Recursively Defined Sequences - Exercises - Page 346: 59

$a_{1}=3$, $a_{n}=2a_{n-1}+1$

First term $a_{1}=3$, Let's look for a pattern. We note that $a_{2}=7=2(3)+1=2a_{1}+1$ $a_{3}= 15=2(7)+1=2a_{2}+1$ $a_{4}=31=2(15)+1=2a_{3}+1$ and so on. So, a recursive rule is $a_{1}=3$, $a_{n}=2a_{n-1}+1$