Question

Tell if each of the following is an arithmetic sequence. find the common difference if it is Arithmetic.

1). 3, 7, 11, 15, 19, ... ____________
2). 4, 16, 64, 56, ... ____________
3). 48, 24, 12, 6, 3, ... ___________
4). 1, 0, -1, -2, -3, .... _____________
5). 9.5, 7.5, 5.5, 3.5, ... ___________

Answer 1

A sequence is arithmetic if it has a constant common difference between terms. The sequences provided display that the first and fourth sequences are arithmetic with common differences of 4 and -1, while the second and third sequences are not arithmetic. The fifth sequence is also arithmetic with a common difference of -2.

Step-by-step explanation:

To determine if a sequence is an arithmetic sequence, we need to check if there is a constant difference between consecutive terms, which is called the common difference.

1. For the sequence 3, 7, 11, 15, 19, ..., we calculate the difference between consecutive terms: 7-3=4, 11-7=4, 15-11=4, and so on. Since this difference is constant, it is an arithmetic sequence with a common difference of 4.
2. The sequence 4, 16, 64, 56, ... does not have a constant difference between terms (16-4=12, 64-16=48, 56-64=-8), so it is not an arithmetic sequence.
3. For the sequence 48, 24, 12, 6, 3, ..., the differences between terms are 24-48=-24, 12-24=-12, 6-12=-6, which are not consistent. Hence, it is not an arithmetic sequence.
4. The sequence 1, 0, -1, -2, -3, ... has differences of 0-1=-1, -1-0=-1, -2-(-1)=-1, which are consistent. Therefore, this is an arithmetic sequence with a common difference of -1.
5. Finally, the sequence 9.5, 7.5, 5.5, 3.5, ... has differences of 7.5-9.5=-2, 5.5-7.5=-2, and 3.5-5.5=-2. Since these differences are constant, it is an arithmetic sequence with a common difference of -2.