Linear number sequences
Generate and describe linear number sequences, including those with negative and decimal steps; identify the term-to-term rule
What a learner can do afterwards
- Continue the sequence 2.5, 4.0, 5.5, ... and state the rule as 'add 1.5'
- Generate terms of a sequence that crosses zero (e.g. 3, 1, −1, −3, ...)
- Describe the term-to-term rule for a given linear sequence and predict the 10th term
The lesson
A sequence is a list of numbers written in order. In a linear sequence, you use the same rule every time to get from one number to the next.
Mia writes 2.5, 4.0, 5.5, 7.0. She checks the gaps: 4.0 minus 2.5 is 1.5, 5.5 minus 4.0 is 1.5, 7.0 minus 5.5 is 1.5. Every gap is the same, so the rule is 'add 1.5'.
Think about a cold day. The temperature is 3, then 1, then -1, then -3. Each step goes down by 2. Even when the numbers cross past zero, the rule stays the same: subtract 2.
To find a term far down the list, you do not need to write out every number. Just keep applying the rule from the term before it, again and again.
A linear sequence always uses the same add or subtract rule, even when the numbers are decimals or cross zero.
Watch it
Where it sits
Learn first
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.