What is the nth term of 2, 6, 2, 6, 2

Answer 1

First, please recognize that:

1. this is not an Arithmetic Sequence (with a constant difference)₂
2. this is not a Geometric Sequence (with a constant ratio)

Only now, recognize that this is a special Sequence with terms that seem to alternate (obviously, only a few terms are presented, so any definition applies only to what's given).

Now, a convenient way to have terms alternate (that is, +1, -1, +1, -1, ...) is to use (-1)ⁿ. The value (range) is connected to that in various ways.

For this problem, one convenient way is to consider the terms to be (4-2), (4+2), (4-2), (4+2), etc.

If the sequence begins with term 1 (note: some start with term 0), we have

a₁ = 2 = 4-2

a₂ = 6 = 4+2

a₃ = 2 = 4-2

a4 = 6 = 4+2

a₅ = 2 = 4-2

...

a_n = 4 + 2*(-1)ⁿ

Note that there may be other formulas (but fewer formulas as there are more terms given that must match.

Answer 2

First, please recognize that:

1. this is not an Arithmetic Sequence (with a constant difference)₂
2. this is not a Geometric Sequence (with a constant ratio)

Only now, recognize that this is a special Sequence with terms that seem to alternate (obviously, only a few terms are presented, so any definition applies only to what's given).

Now, a convenient way to have term alternate (that is, +1, -1, +1, -1, ...) is to use (-1)ⁿ. The value (range) is connected to that in various ways.

For this problem, one convenient way is to consider the terms to be (4-2), (4+2), (4-2), (4+2), etc.

If the sequence begins with term 1 (note: some start with term 0), we have

a₁ = 6 = 4+2

a₂ = 2 = 4-2

a₃ = 6 = 4+2

a4 = 2 = 4-2

a

a₄ = 2 = 4-2

a₅ = 6 = 4+2

...

a_n = 4 + 2*(-1)ⁿ

Note that there may be other formulas (but fewer formulas as there are more terms given that must match.