Final answer:
The given series 13, 55, 97, 139 demonstrates a constant difference of 42 between consecutive terms, indicating that it is an arithmetic sequence. The quotients between successive terms are not consistent, so it is not a geometric sequence.
Step-by-step explanation:
To determine if the given series 13, 55, 97, 139 is an arithmetic or a geometric sequence, we need to analyze the pattern in its terms. An arithmetic sequence is a sequence of numbers with the same difference between consecutive terms, whereas a geometric sequence has a common ratio between consecutive terms.
Let's check for an arithmetic progression first:
55 - 13 = 42
97 - 55 = 42
139 - 97 = 42
In this sequence, the difference between each pair of consecutive terms is consistently 42. This consistent difference indicates that the sequence is arithmetic.
For a geometric sequence, we would need to divide consecutive terms and find the same quotient:
55 / 13 ≈ 4.23
97 / 55 ≈ 1.76
139 / 97 ≈ 1.43
The quotients are not the same; hence, the sequence is not geometric.
Based on the calculations, the answer is A) Arithmetic Sequence, as the sequence has a constant difference of 42 between consecutive terms.