NY Next Generation Math AII-F.BF.2
The Standard
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students write arithmetic and geometric sequences in Algebra II both recursively and explicitly using subscript notation. They model situations and translate accurately between the two forms.
What Mastery Looks Like
- The student includes the initial term, common difference or ratio, and correct index shift. Recursive and explicit rules produce the same selected terms and fit the context.
Common Misconceptions
- Students may omit the starting term, confuse difference with ratio, or use n instead of n minus 1 for a sequence beginning at one. They may translate a geometric sequence as linear.
How to Assess It
- A sequence begins at 6 and triples each term. Ask students for recursive and explicit rules in subscript notation and terms one, four, and seven.
Lesson moves
Ways to Teach It
Build sequences with term cards, then attach recursive and explicit rule cards that generate the same values.
Ask students how the starting index determines whether an explicit exponent uses n or n minus 1.
Play sequence translation by converting arithmetic and geometric rules between recursive, explicit, table, and context forms.
Model annual deposits or repeated percent growth with both recursive and explicit sequence definitions.
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Printable AII-F.BF.2 Worksheet
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