How this calculation works
Changing the spacing between observations changes the interpretation. The rule assumes the steps are equally spaced.
Next term = 3u₃ − 3u₂ + u₁A worked example
For 2, 5, 10, first differences are 3 and 5. The next difference is 7, giving 17.
Good to know
Three observations alone do not establish a unique general sequence.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Predict the next equally spaced term assuming the second difference stays constant.
The primary result is labeled “Next term”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Three observations alone do not establish a unique general sequence.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
For 2, 5, 10, first differences are 3 and 5. The next difference is 7, giving 17.
Which rule does this calculator apply?
Next term = 3u₃ − 3u₂ + u₁