How this calculation works
The recurrence determines later terms from the two starting values. Choosing index zero or one returns a supplied starting value.
THE FORMULA
uₙ = a uₙ₋₁ + b uₙ₋₂A worked example
Starting at 2 and 3 with uₙ = 2uₙ₋₁ − uₙ₋₂ gives u₅ = 7.
Good to know
The first term is indexed by zero.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Calculate a term of a second-order recurrence from two starting values.
The primary result is labeled “Target term”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The first term is indexed by zero.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
Starting at 2 and 3 with uₙ = 2uₙ₋₁ − uₙ₋₂ gives u₅ = 7.
Which rule does this calculator apply?
uₙ = a uₙ₋₁ + b uₙ₋₂