State whether the following sequence is arithmetic, geometric, or neither.
4, 15, 26, 37, 48, 59, .....
Arithmetic, the common difference is 11.
15 - 4 = 11
26 - 15 = 11
37 - 26 = 11
48 - 37 = 11
59 - 48 = 11
To determine whether a sequence is arithmetic, geometric, or neither, we need to analyze the differences between consecutive terms.
Let's calculate the differences between the terms:
15 - 4 = 11
26 - 15 = 11
37 - 26 = 11
48 - 37 = 11
59 - 48 = 11
From the calculations above, we can see that the differences between consecutive terms are always 11.
In an arithmetic sequence, the differences between consecutive terms are constant. Since the differences in this sequence are constant (11), we can conclude that the given sequence is an arithmetic sequence.