Induction on number sequences

For each of the sequences below, the corresponding activity will lead you to explore the nature of induction proofs.

• 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 = a_n-1 + (n + 4) with a₁ = 3.