is the sequence below arithmetic geometric or neither

Question

5,10,20,25

Answer 1

To determine whether the sequence \(5, 10, 20, 25\) is arithmetic, geometric, or neither, we can analyze it as follows:

1. Arithmetic Sequence: In an arithmetic sequence, the difference between consecutive terms is constant. Let's find the differences:

   • \(10 - 5 = 5\)
   • \(20 - 10 = 10\)
   • \(25 - 20 = 5\)

   The differences are \(5, 10, 5\), which are not constant. Therefore, the sequence is not arithmetic.

2. Geometric Sequence: In a geometric sequence, the ratio between consecutive terms is constant. Let's find the ratios:

   • \(\frac{10}{5} = 2\)
   • \(\frac{20}{10} = 2\)
   • \(\frac{25}{20} = 1.25\)

   The ratios are \(2, 2, 1.25\), which are not constant. Therefore, the sequence is not geometric.

Since the sequence does not satisfy the criteria for either an arithmetic or a geometric sequence, we can conclude that it is neither.