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Nth-Term Rules

PROCEDURAL
MathematicsAlgebra|Ages 12—14|ID: mt_HRKzwEQJgO

Find the nth-term expression for an arithmetic sequence by identifying the common difference and the zero-term, and use it to determine any term in the sequence or test whether a given number belongs to the sequence

Mastery Evidence

  • Derive the nth-term rule for an arithmetic sequence such as 3, 7, 11, 15, … as 4n − 1
  • Use an nth-term formula to find the 50th or 100th term without listing all preceding terms
  • Determine whether a given number (e.g., 99) is a term in a specified arithmetic sequence

Assessment Prompt

“If [child] is given the sequence 4, 7, 10, 13…, can they find a formula for the nth term — and use it to check whether, say, 100 is in the sequence?”

Curriculum Standards2 alignments

8.F.4Common Core State Standards for Mathematics
Constructing linear functions

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

F
KS3.Maths.Alg.15The national curriculum in England
Arithmetic Sequences

recognise arithmetic sequences and find the nth term

Mathematics · Key Stage 3

Prerequisites2

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