Sequences & series

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Standard

   A sequence is defined recursively by $a_{1} = -1$ and $a_{n+1} = a_{n} + 4$ for $n \ge 1$. When this sequence is rewritten with an explicit formula of the form $a_{n} = An + B$, what is the value of $B$?

2. Standard

   A sequence is defined recursively by $a_{1} = 3$ and $a_{n+1} = a_{n} + 9$ for $n \ge 1$. When this sequence is rewritten with an explicit formula of the form $a_{n} = An + B$, what is the value of $B$?

3. Standard

   A sequence is defined recursively by $a_{1} = -6$ and $a_{n+1} = a_{n} + 2$ for $n \ge 1$. When this sequence is rewritten with an explicit formula of the form $a_{n} = An + B$, what is the value of $B$?

Problems shown under their original terms: Generated (template, solver-computed).