Recursive Sequences

For each of the sequences below, the corresponding activity will lead you to explore the nature of the recursive definition as well as some patterns among the terms of the sequence.

• Sequence 1. a_n = a_n-1 + 2n with a₁ = 2.
• Sequence 2. a_n = a_n-1 + (2n - 1) with a₁ = 1.
• Sequence 3. a_n = a_n-1 + (n + 4) with a₁ = 5.
• Sequence 4. a_n = 2a_n-1 + 1 with a₁ = 1.