Decide whether a sequence is arithmetic, geometric or neither

The list begins 4, 8, 12, 17. Does checking only 8 − 4 establish an arithmetic pattern?

The first three terms are 4, 8 and 12. The last term is 16 plus the slider setting. Adjust it and watch the differences. Find the setting where they all agree

Which slider setting makes this list arithmetic?

Two tests, applied carefully

An arithmetic sequence has a constant difference. A geometric sequence repeats a multiplier. For the nonzero lists here, compare every later-to-earlier ratio

1. 1Arithmetic Check that all later-minus-earlier differences agree
2. 2Geometric For nonzero preceding terms, check that all later-divided-by-earlier ratios agree
3. 3Neither If both tests fail, the displayed list is neither

Classify 3, 7, 11, 15.

Given values

\(\displaystyle 3,7,11,15\)

For 3, 7, 11, 15, find the common difference

Classify 8, 12, 18, 27.

Given values

\(\displaystyle 8,12,18,27\)

For 8, 12, 18, 27, find the common ratio

Classify 2, 5, 9, 14.

Vary the multiplier for a sequence starting at 8. Compare positive decay, a constant sequence and alternating signs. Use the readouts to check the rule

At multiplier 1, how can the nonzero constant sequence be described?

The nonzero constant list is 5, 5, 5, 5. Which statement is correct?

A list contains 0. Can you blindly divide by every preceding term?

For 18, 9, 4.5, 2.25, the common ratio is:

Classify the displayed pattern

Check every pair of neighbouring terms. A few terms can fit more than one rule, so do not assume that the first pair tells the whole story

1. 1Practice scope These practice lists use positive values that do not stay constant, so exactly one of the three labels applies
2. 2Explain your choice Show the repeated difference or ratio, or show why both tests fail. Choosing a label is not the same as explaining why