Common Core · High school
HSF-BF.A.2
High school — Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
The 2 skills that cover it
- Arithmetic & Geometric SequencesSee a list of numbers as a function of its position: tell an arithmetic sequence from a geometric one, write explicit and recursive formulas, and find any term without listing the ones before it.Read the lesson →
- Series & Sigma NotationAdd the terms of a sequence without adding them one by one: the arithmetic series formula, the finite geometric series formula, sigma notation, and the infinite geometric series that settles on a value.Read the lesson →
What a student should be able to do
- Identify a sequence as arithmetic or geometric and find its common difference or ratio.
- Write an explicit formula for the nth term and use it to find a given term.
- Write and use a recursive formula, and convert between recursive and explicit forms.
- Find a formula from two given terms.
- Find the sum of the first n terms of an arithmetic series.
- Find the sum of the first n terms of a geometric series.
- Read and write a series in sigma notation and evaluate it.
- Decide whether an infinite geometric series converges and find its sum.