Linear number sequences

Mathematics · Algebra · ages 10-11

Name ______________________ Date ____________

What is the rule for 2.5, 4.0, 5.5?
- Add 1.5 each time
- Add 2.5 each time
- Add 1 each time
- Multiply by 1.5 each time
The sequence 2.5, 4.0, 5.5 continues with the same rule. What is the next term?
Answer: ______________
What is the term-to-term rule for 5, 8, 11, 14?
- add 2
- add 3
- add 4
The rule 'add 1.5' means each new term is 1.5 more than the one before it.
Circle one: True False
A sequence is 8, 5, 2, -1, ... What is the next term?
- -2
- -3
- -4
Gwen says 2.5, 4.0, 5.5, 7.0, 8.5 continues the pattern. Is Gwen right?
Circle one: True False
What is the 6th term of 3, 1, -1, -3, ...?
Answer: ______________
A sequence starts at 3 and the rule is 'subtract 2'. What is the 4th term?
Answer: ______________
Ivy says the sequence 6, 9, 12, 16 follows the rule 'add 3'. Is she right?
- Yes, every gap is 3
- No, the last gap is 4, not 3
- No, the first gap is not 3
A sequence starts at 100 and subtracts 6 each time. What is the 6th term?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

Add 1.5 each time · Each term is 1.5 more than the one before.
7 · 5.5 + 1.5 = 7.
add 3 · Check the gap between terms: 8 minus 5 is 3, and 11 minus 8 is 3. The rule is add 3.
True · That is exactly what a term-to-term rule means: the same amount is added every time.
-4 · The rule is subtract 3. Subtracting 3 from -1 gives -4, even after crossing zero.
True · Gwen is right: each new term adds 1.5.
-7 · 3 - 5 x 2 = -7.
-3 · Keep subtracting 2: 3, 1, -1, -3. The sequence crosses zero but the rule never changes.
No, the last gap is 4, not 3 · The first two gaps are 3, but 16 minus 12 is 4. A true rule needs the same gap every time.
70 · 100 - 5 x 6 = 70.