The nth term

The Maths Habit
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A sequence goes 4, 7, 10, 13, … What is the 100th term? How could you find it without writing out every term?

301

Position
Where a term is in the sequence.
nth term
A rule that gives any term from its position, n.

n12345
Sequence47101316
3n3691215

Find the nth term

10, 17, 24, 31, …

Find the nth term

n12345
Sequence1591317
4n

Find the nth term of the sequence 8, 14, 20, 26, …

8n = 114n = 220n = 326n = 46+612+618+624+2times table row underneath
goes up by 6, so 6n
6n + 2 matches
Answer6n + 2

Find the nth term of the sequence 3, 11, 19, 27, …

3n = 1+811n = 2+819n = 3+827n = 48162432−5times table row underneath
goes up by 8, so start with 8n
8n − 5 matches
Answer8n − 5

Find the nth term of the sequence 8, 14, 20, 26, …

8n = 114n = 220n = 326n = 46+612+618+624+2times table row underneath
goes up by 6, so 6n
6n + 2 matches
Answer6n + 2

Find the nth term of the sequence 12, 21, 30, 39, …

12n = 121n = 230n = 339n = 49+918+927+936+3times table row underneath
goes up by 9, so 9n
9n + 3 matches
Answer9n + 3

Find the nth term of the sequence 8, 14, 20, 26, …

8n = 114n = 220n = 326n = 46+612+618+624+2times table row underneath
goes up by 6, so 6n
6n + 2 matches
Answer6n + 2

Find the nth term of the sequence 4, 9, 14, 19, …

4n = 19n = 214n = 319n = 45+510+515+520−1times table row underneath
goes up by 5, so 5n
5n − 1 matches
Answer5n − 1

Find the nth term of the sequence 8, 14, 20, 26, …

8n = 114n = 220n = 326n = 46+612+618+624+2times table row underneath
goes up by 6, so 6n
6n + 2 matches
Answer6n + 2

Find the nth term of the sequence 11, 13, 15, 17, …

11n = 113n = 215n = 317n = 42+24+26+28+9times table row underneath
goes up by 2, so 2n
2n + 9 matches
Answer2n + 9

Find the nth term of the sequence 8, 14, 20, 26, …

8n = 114n = 220n = 326n = 46+612+618+624+2times table row underneath
goes up by 6, so 6n
6n + 2 matches
Answer6n + 2

Find the nth term of the sequence 3, 13, 23, 33, …

3n = 113n = 223n = 333n = 410+1020+1030+1040−7times table row underneath
goes up by 10, so 10n
10n − 7 matches
Answer10n − 7

The nth term of a linear sequence worksheet, page 1

The nth term of a linear sequence worksheet, page 2

Answer sheet

  1. The nth term of a sequence is 4n + 3. Is 50 in the sequence? How do you know?

    No: 47 and 51 are

  2. Find the nth term of this sequence, which goes down:  20, 17, 14, 11, …

    23 − 3n

  1. Find the nth term of 5, 9, 13, 17, …

    4n + 1

  2. Find the nth term of 4, 11, 18, 25, …

    7n − 3

  3. The nth term of a sequence is 5n + 2. Is 74 in the sequence? Explain how you know.

    No: 72 and 77 are
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