Question

classify the following sequence:
1, 3, 6, 10, 15, ...
geometric
neither
arithmetic

Explanation:

Step1: Check for arithmetic sequence

An arithmetic sequence has a common difference. Let's find the differences between consecutive terms:
\(3 - 1 = 2\)
\(6 - 3 = 3\)
\(10 - 6 = 4\)
\(15 - 10 = 5\)
The differences (2, 3, 4, 5,...) are not constant, so it's not arithmetic.

Step2: Check for geometric sequence

A geometric sequence has a common ratio. Let's find the ratios between consecutive terms:
\(\frac{3}{1} = 3\)
\(\frac{6}{3} = 2\)
\(\frac{10}{6} = \frac{5}{3}\)
\(\frac{15}{10} = \frac{3}{2}\)
The ratios are not constant, so it's not geometric.

Answer:

neither