Question

Identify if the following is an arithmetic sequence or a quadratic sequence. if the given is not a sequence, write, "not a sequence". 1, 5/4, 3/2, 7/4,… 17, 31, 49, 71,…. 5, 27, 49, 71,… 30, 27, 22, 15 2, 45, 68, 79,….

Answer 1

The first given sequence is an arithmetic sequence with a common difference of 1/4. The second and third sequences do not have a clear pattern and are not sequences. The fourth and last sequence is a quadratic sequence with a formula of f(n) = 2n^2 + 3n - 2.

Step-by-step explanation:

The given sequences are:

1. 1, 5/4, 3/2, 7/4,... - This is an arithmetic sequence because the difference between consecutive terms is constant. The common difference is 1/4.
2. 17, 31, 49, 71,... - This is not a sequence because there is no clear pattern or common difference. Therefore, it is not a sequence.
3. 5, 27, 49, 71,... - This is not a sequence because there is no clear pattern or common difference. Therefore, it is not a sequence.
4. 30, 27, 22, 15 - This is not a sequence because there is no clear pattern or common difference. Therefore, it is not a sequence.
5. 2, 45, 68, 79,... - This is a quadratic sequence because the difference between consecutive terms is not constant, but the difference of the differences is constant. The equation for this sequence is f(n) = 2n^2 + 3n - 2.