Sequences: counting in steps

The Maths Habit Handout to print

Someone crosses the stones, making the same jump every time. Where does the next footprint go?

Three stones on: the same jump again.

Sequence
Numbers in order that follow a rule.
Term
One number in a sequence.
Jump
How much it goes up or down from one term to the next.
Rule
What you do to get the next term.

25811+3+3+314+3
  1. Find the jump.Count from one term to the next. Going up, add. Going down, take away.
  2. Keep making the same jump.Say the rule in words: add 3 each time.

What is the jump?

10, 12, 14, 16 +2: add 2 each time

What is the jump?

30, 25, 20, 15 −5: take away 5 each time

4, 7, 10, 13, , Find the missing terms.
Find the jump.
Keep making the same jump. 16, 19

4710131619+3+3+3+3+3

6, 10, 14, 18, , Find the missing terms.
Find the jump.
Keep making the same jump. 22, 26

6101418+42226+4+4+4+4

4, 7, 10, 13, , Find the missing terms.
Find the jump.
Keep making the same jump. 16, 19

4710131619+3+3+3+3+3

40, 35, 30, 25, , Find the missing terms.
Find the jump.
Keep making the same jump. 20, 15

403530252015−5−5−5−5−5

4, 7, 10, 13, , Find the missing terms.
Find the jump.
Keep making the same jump. 16, 19

4710131619+3+3+3+3+3

3, 9, 15, 21, , Find the missing terms.
Find the jump.
Keep making the same jump. 27, 33

391521+62733+6+6+6+6

4, 7, 10, 13, , Find the missing terms.
Find the jump.
Keep making the same jump. 16, 19

4710131619+3+3+3+3+3

50, 42, 34, 26, , Find the missing terms.
Find the jump.
Keep making the same jump. 18, 10

504234261810−8−8−8−8−8

4, 7, 10, 13, , Find the missing terms.
Find the jump.
Keep making the same jump. 16, 19

4710131619+3+3+3+3+3

Start at 7. Add 4 each time.Write the first five terms.
Keep making the same jump. 7, 11, 15, 19, 23

711151923+4+4+4+4

Sequences: counting in steps worksheet, page 1

What comes after 0?

6, 4, 2, 0, ... −2

Find the missing term.

5152010+5+5+5 10

8, 5, 2, , , Find the missing terms.
Find the jump.
Keep making the same jump. −1, −4, −7

852−1−4−7−3−3−3−3−3

6, 2, −2, , , Find the missing terms.
Find the jump.
Keep making the same jump. −6, −10, −14

62−2−4−6−10−14−4−4−4−4

8, 5, 2, , , Find the missing terms.
Find the jump.
Keep making the same jump. −1, −4, −7

852−1−4−7−3−3−3−3−3

−10, −7, −4, , Find the missing terms.
Find the jump.
Keep making the same jump. −1, 2

−10−7−4−12+3+3+3+3

Sequences: counting in steps worksheet, page 2

Answer sheet

Is the last term right? Thumbs up or down.

  1. 2, 5, 8, 11

    Right

  2. 20, 16, 12, 9

    Wrong: 8

  3. 3, 1, −1, −3

    Right

  4. −6, −4, −2, 2

    Wrong: 0

  5. 15, 10, 5, 0

    Right

  1. The 1st term is 3 and the rule is add 4 each time. What is the 10th term?

    39

  2. Make a sequence where the 1st term is 20 and the 5th term is 0.

    20, 15, 10, 5, 0

  3. A sequence goes 1, 4, 7, ... Is 100 in it? How do you know?

    Yes: 99 is 33 jumps of 3

  1. Find the next two terms: 6, 11, 16, 21. Find the jump. Keep making the same jump.

    26, 31

  2. Write the rule for 20, 17, 14, 11.

    take away 3 each time

  3. Find the missing terms: 8, 4, , , −8. Find the jump. Keep making the same jump.

    0, −4
    84−8
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