Answer:
Ok, here we have the sequence:
0.25, 1.75, 3.75, 5.75, 7.75, …
First let's define the two most common types of sequences:
Arithmetic: The difference between any two consecutive terms of the sequence is always the same.
Geometric: In this case, the terms are created by multiplicating the previous term by a constant number (and this is for all the terms in the sequence).
Now let's try to see if this is arithmetic, to do it, we select different sets of two consecutive terms and see their difference, if all the differences are the same, then this is an arithmetic sequence:
1.75 - 0.25 = 1.5
3.75 - 1.75 = 2
5.75 - 3.75 = 2
So for the first two terms, the difference is 1.5 and for all the next ones, the difference is 2, then it is not an arithmetic sequence.
(it would be if the first term was -0.25 instead of 0.25).
Now let's try with geometric.
To see if the series is geometric, we should see the quotient of consecutive pairs of numbers, if this quotient is the same for all of them, then this is a geometric sequence:
1.75/0.25 = 7
3.75/1.75 = 2.14
Well, we can see that the quotients are different, then this can not be a geometric sequence.
Then the answer will be neither.
If we want to write a recursive rule will be like an arithmetic sequence, but with the first two terms specified as:
a₀ = 0.25
a₁ = 1.75
aₙ = aₙ₋₁ + 2 for n = 2, 3, 4, .......
