State whether the following sequence is arithmetic, geometric, or neither.
0, 1, 4, 9, 16, 25, 36, ....
Each is the square of the base number, 0^2, 1^2, 2^2, 3^2,....
What does that tell you?
neither
To determine if the given sequence is arithmetic, geometric, or neither, we need to identify the pattern or rule governing the terms.
To do this, we can examine the differences between consecutive terms to check if they form a constant pattern. Let's calculate the differences between consecutive terms in the given sequence:
1 - 0 = 1
4 - 1 = 3
9 - 4 = 5
16 - 9 = 7
25 - 16 = 9
36 - 25 = 11
Since the differences between consecutive terms (1, 3, 5, 7, 9, 11) are not the same, the sequence is not arithmetic.
To check if the sequence is geometric, we can compute the ratios of consecutive terms:
1 / 0 = undefined
4 / 1 = 4
9 / 4 = 2.25
16 / 9 ≈ 1.78
25 / 16 ≈ 1.56
36 / 25 ≈ 1.44
As the ratios are not constant, the sequence is not geometric either.
Therefore, based on the calculations, we can conclude that the given sequence (0, 1, 4, 9, 16, 25, 36, ...) is neither arithmetic nor geometric, as there is no consistent pattern or rule observed.