Sure, here are the recurrence relations for each of the sequences:

a) For the sequence an = 3, a simple recurrence relation is an = a(n-1). This is because every term in the sequence is 3, so each term is equal to the previous term.

b) For the sequence an = n^2 + n, a possible recurrence relation is an = (n-1)^2 + (n-1) + 2n. This is derived from the fact that n^2 = (n-1)^2 + 2n - 1.

c) For the sequence an = n + (-1)^n, a possible recurrence relation is an = a(n-1) + 2 if n is even, and an = a(n-1) if n is odd. This is because when n is even, (-1)^n = 1, and when n is odd, (-1)^n = -1. So, the sequence increases by 2 for every even term and stays the same for every odd term.

Question

Sure, here are the recurrence relations for each of the sequences:

a) For the sequence an = 3, a simple recurrence relation is an = a(n-1). This is because every term in the sequence is 3, so each term is equal to the previous term.

b) For the sequence an = n^2 + n, a possible recurrence relation is an = (n-1)^2 + (n-1) + 2n. This is derived from the fact that n^2 = (n-1)^2 + 2n - 1.

c) For the sequence an = n + (-1)^n, a possible recurrence relation is an = a(n-1) + 2 if n is even, and an = a(n-1) if n is odd. This is because when n is even, (-1)^n = 1, and when n is odd, (-1)^n = -1. So, the sequence increases by 2 for every even term and stays the same for every odd term.

Knowee AI · Accepted Answer

Sure, here are the recurrence relations for each of the sequences:

a) For the sequence an = 3, a simple recurrence relation is an = a(n-1). This is because every term in the sequence is 3, so each term is equal to the previous term.

b) For the sequence an = n^2 + n, a possible recurrence relation is an = (n-1)^2 + (n-1) + 2n. This is derived from the fact that n^2 = (n-1)^2 + 2n - 1.

c) For the sequence an = n + (-1)^n, a possible recurrence relation is an = a(n-1) + 2 if n is even, and an = a(n-1) if n is odd. This is because when n is even, (-1)^n = 1, and when n is odd, (-1)^n = -1. So, the sequence increases by 2 for every even term and stays the same for every odd term.

For each of these sequences find a recurrence relation satisfied by this sequence. (Theanswers are not unique because there are infinitely many different recurrence relations satisfied byany sequence.)a) an=3b) an = n2 + nc) an = n + (−1)n

Question

Solution

Similar Questions

Upgrade your grade with Knowee