Question

Determine the type of sequence for the following series: 13, 55, 97, 139. Is it an arithmetic sequence or geometric sequence?**

A) *Arithmetic Sequence*

B) *Geometric Sequence*

C) *Neither Arithmetic nor Geometric*

D) *Both Arithmetic and Geometric*

Answer 1

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.