Try to use kth differences to find a closed form for the

Question

Question: 1. Try to use kth differences to find a closed form for the recurrence a₀ = 1, a_n = 2a_n-1. What happens?

2. Try to use kth differences to find a closed form for the recurrence a0 = 0, an = a_n-1 +n(-1)ⁿ. What happens?

3. Find a closed form for a₀ = 8, a_n = a_n-1 -4 and check that your formula is correct.

4. Find a closed form for a₀ = 3, a_n = a_n-1 +2 and check that your formula is correct.

5. Challenge: Create your own recurrence for which a closed form can be found using kth differences, and find that closed form.