Question

Which representation yields the same outcome as the sequence defined recursively below?

a₁ = 3
an −4+ an - 1
PLEASE HURRY​

Answer 1

The equivalent representation of the given sequence is a_n = (-1)^n * (n + 1).

Step-by-step explanation:

The given sequence is defined recursively as follows:

a1 = 3

an = an-1 - 4 + an-2

To find an equivalent representation, we can start with the first few terms and look for a pattern. The given sequence can be rewritten as:

a1 = 3

a2 = 3 + (-4) + 3 = 2

a3 = 2 + (-4) + 3 = 1

a4 = 1 + (-4) + 2 = -1

a5 = -1 + (-4) + 1 = -4

a6 = -4 + (-4) + (-1) = -9

Based on this pattern, we can conclude that the equivalent representation of the given sequence is:

an = (-1)^n * (n + 1), n ≥ 1