Which type of sequence is represented by the numbers 25, 31, 37, 43?

Which type of sequence is represented by the numbers 25, 31, 37, 43?

• A. Geometric
• B. Arithmetic
• C. Neither
• D. Exponential

Answer: (B)

The sequence represented by the numbers 25, 31, 37, 43 is an arithmetic sequence. An arithmetic sequence is defined as a sequence of numbers in which the difference between consecutive terms is constant. In this case, you can observe the differences between successive terms: - From 25 to 31, the difference is 6 (31 - 25 = 6). - From 31 to 37, the difference is also 6 (37 - 31 = 6). - From 37 to 43, the difference continues to be 6 (43 - 37 = 6). Since the difference of 6 is consistent throughout the sequence, it confirms that this is indeed an arithmetic sequence. Each term is generated by adding the same fixed amount, 6, to the previous term. This consistent pattern of adding or subtracting a constant amount characterizes arithmetic sequences. In contrast, a geometric sequence involves multiplying a constant factor to obtain the next term, while exponential growth refers to sequences where terms increase by a consistent percentage or factor over time. Neither of these definitions applies to the given sequence, clearly identifying it as arithmetic.

The sequence represented by the numbers 25, 31, 37, 43 is an arithmetic sequence. An arithmetic sequence is defined as a sequence of numbers in which the difference between consecutive terms is constant.

In this case, you can observe the differences between successive terms:

• From 25 to 31, the difference is 6 (31 - 25 = 6).

• From 31 to 37, the difference is also 6 (37 - 31 = 6).

• From 37 to 43, the difference continues to be 6 (43 - 37 = 6).

Since the difference of 6 is consistent throughout the sequence, it confirms that this is indeed an arithmetic sequence. Each term is generated by adding the same fixed amount, 6, to the previous term. This consistent pattern of adding or subtracting a constant amount characterizes arithmetic sequences.

In contrast, a geometric sequence involves multiplying a constant factor to obtain the next term, while exponential growth refers to sequences where terms increase by a consistent percentage or factor over time. Neither of these definitions applies to the given sequence, clearly identifying it as arithmetic.