L1 · Arithmetic Sequences in Tables of Values

Learning goal

“I can recognize an arithmetic sequence - one where the same amount is added or subtracted at every step - record it in a table of values with position and term, and find the next terms and missing terms by using the constant difference.”

Arithmetic sequence — an ordered list of numbers where you add (or subtract) the SAME amount to get from each number to the next. 4, 7, 10, 13 is arithmetic; 3, 6, 12, 24 is not.

Position — the place of a number in the sequence: 1st, 2nd, 3rd, ... Positions are counted 1, 2, 3, 4, ...

Term — the number sitting at a position. In 4, 7, 10, 13, the term at position 3 is 10.

Table of values — a chart pairing each position with its term: position in the first column, term in the second.

Constant difference — the amount added (or subtracted) at every step. For 4, 7, 10, 13 the constant difference is +3.

Worked example

Study the sequence 4, 7, 10, 13. Step 1: Measure the gaps: 7 - 4 = 3, 10 - 7 = 3, 13 - 10 = 3. Every gap is 3 - the constant difference is +3, so this IS an arithmetic sequence. Step 2: Pour it into a table of values. Position | Term: 1 | 4, 2 | 7, 3 | 10, 4 | 13. Position counts the place; term is the number in that place. Step 3: Extend: the next term is 13 + 3 = 16 (position 5); then 19 (position 6). Say it plainly: "arithmetic" is a promise - the gap NEVER changes. Check every gap before trusting a sequence; one broken gap breaks the promise.

Check yourself — explain it

The sequence 5, 9, 13, 17 is arithmetic because...

Paired problem — example still visible

Sequence 6, 11, 16, 21: gaps are 11 - 6 = 5, 16 - 11 = 5, 21 - 16 = 5 -> constant difference +5; next term = 26

Faded completion — last step is yours

"Sequence 9, 13, 17, 21: gaps are 4, 4, 4, so the next term is 21 + ___ = ___" -> 4; 25

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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