Mathematics Algebra Procedural 12–14 yrs

Nth-Term Rules

第n项规则

Description

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 your 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?