Hello! i am stuck on this recursive definition. I don't know what to do next.

Q: Give a recursive definition of the sequence {an}, n = 1, 2, 3, … if

a.) an = 4n – 2

b.) an = 1 + (-1)^(n)

c.) an = n(n + 1)

d.) an = n²

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I have this:

a.)

an = 4n – 2

a1 = 4(1) – 2

a1 = 4 – 2

a1 = 2

an = 4n – 2

a2 = 4(2) – 2

a2 = 8 - 2

a2 = 6

an = 4n – 2

a3 = 4(3) – 2

a3 = 12 - 2

a3 = 10

an = 4n – 2

a4 = 4(4) – 2

a4 = 16 - 2

a4 = 14

I can see they go up by 4 for part a, but do i leave it like this?

b.)

an = 1 + (-1)^(n)

a1 = 1 + (-1)^(1)

a1 = 1 – 1

a1 = 0

an = 1 + (-1)^(n)

a2 = 1 + (-1)^(2)

a2 = 1 + 1

a2 = 2

an = 1 + (-1)^(n)

a3 = 1 + (-1)^(3)

a3 = 1 – 1

a3 = 0

an = 1 + (-1)^(n)

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

a4 = 1 + 1

a4 = 2

I can see the sequence going 0, 2, 0, 2, ... etc.

c.)

an = n(n + 1)

a1 = 1(1 + 1)

a1 = 1(2)

a1 = 2

an = n(n + 1)

a2 = 2(2 + 1)

a2 = 2(3)

a2 = 6

an = n(n + 1)

a3 = 3(3 + 1)

a3 = 3(4)

a3 = 12

an = n(n + 1)

a4 = 4(4 + 1)

a4 = 4(5)

a4 = 20

I am not sure on this one?