The nth term of a linear sequence

The Maths Habit

How many chairs are needed for 10 tables? Can you find out without drawing them all?

1 table2 tables3 tables

22 chairs

Position
Where a term is in the sequence.
n1234
nth term
A rule that gives any term from its position, n.
n1234+ gap+ gap+ gap+ gapnhopnth term =hopn+gap

n1234+ gap+ gap+ gap+ gap2n1
  1. 1Write the times table.3n means 3 × n: the 3 times table.
  2. 2Add the gap.Add the same number to every one.

The nth term is 3n + 2. Write the first four terms.

n1234581114+2+2+2+22Add the gap.3n369121Write the times table.

The nth term is 2n + 6. Write the first four terms.

n12348101214+6+6+6+62Add the gap.2n24681Write the times table.

The nth term is 3n + 2. Write the first four terms.

n1234581114+2+2+2+22Add the gap.3n369121Write the times table.
1Write the times table.
2Add the gap.

The nth term is 5n + 1. Write the first four terms.

n12346111621+1+1+1+12Add the gap.5n51015201Write the times table.

The nth term is 3n + 2. Write the first four terms.

n1234581114+2+2+2+22Add the gap.3n369121Write the times table.
1Write the times table.
2Add the gap.

The nth term is 10n + 3. Write the first four terms.

n123413233343+3+3+3+32Add the gap.10n102030401Write the times table.

The nth term is 3n + 2. Write the first four terms.

n1234581114+2+2+2+22Add the gap.3n369121Write the times table.
1Write the times table.
2Add the gap.

The nth term is 3n + 5. Write the first four terms.

n12348111417+5+5+5+52Add the gap.3n369121Write the times table.

1Write the times table.
2Add the gap.

1The nth term is 2n + 10. Write the first four terms.

n123412141618+10+10+10+102n2468

2The nth term is 3n + 1. Write the first four terms.

n1234471013+1+1+1+13n36912

3The nth term is 5n + 5. Write the first four terms.

n123410152025+5+5+5+55n5101520

4The nth term is 10n + 2. Write the first four terms.

n123412223242+2+2+2+210n10203040

How big is the hop?

n12+347
n12+5611
n12+101424

n1234+ hop+ hop+ hop1+ gap+ gap+ gap+ gap3nhop2nth term =hopn+gap4
  1. 1Find the hop.The same every time.
  2. 2Write the times table.The hop tells you which one.
  3. 3Find the gap.From the times table up to the term.
  4. 4Write the nth term.hop n + gap

Find the nth term.

n1234+4+4+41Find the hop.7111519+3+3+3+33Find the gap.n44812162Write the times table.nth term =4n+34Write the nth term.

Find the nth term.

n1234+2+2+21Find the hop.46810+2+2+2+23Find the gap.n224682Write the times table.nth term =2n+24Write the nth term.

Find the nth term.

n1234+4+4+41Find the hop.7111519+3+3+3+33Find the gap.n44812162Write the times table.nth term =4n+34Write the nth term.
1Find the hop.
2Write the times table.
3Find the gap.
4Write the nth term.

Find the nth term.

n1234+5+5+51Find the hop.9141924+4+4+4+43Find the gap.n551015202Write the times table.nth term =5n+44Write the nth term.

Find the nth term.

n1234+4+4+41Find the hop.7111519+3+3+3+33Find the gap.n44812162Write the times table.nth term =4n+34Write the nth term.
1Find the hop.
2Write the times table.
3Find the gap.
4Write the nth term.

Find the nth term.

n1234+10+10+101Find the hop.15253545+5+5+5+53Find the gap.n10102030402Write the times table.nth term =10n+54Write the nth term.

Find the nth term.

n1234+4+4+41Find the hop.7111519+3+3+3+33Find the gap.n44812162Write the times table.nth term =4n+34Write the nth term.
1Find the hop.
2Write the times table.
3Find the gap.
4Write the nth term.

Find the nth term.

n1234+3+3+31Find the hop.9121518+6+6+6+63Find the gap.n3369122Write the times table.nth term =3n+64Write the nth term.

The nth term worksheet, page 1

The nth term worksheet, page 2

Answer sheet

Is it right?
Thumbs up: right. Thumbs down: wrong.

  1. 4, 7, 10, 13. The nth term is 3n + 1.

    Right

  2. 5, 7, 9, 11. The nth term is n + 2.

    Wrong: it is 2n + 3

  3. The nth term is 5n + 1. The first term is 6.

    Right

  4. 6, 10, 14, 18. The nth term is 4n + 6.

    Wrong: it is 4n + 2

  5. The nth term is 2n + 5. The 2nd term is 9.

    Right

  1. Find the nth term of 2, 7, 12, 17, …

    5n − 3

  2. Is 50 in the sequence 4n + 3? How do you know?

    No: 47 and 51 are, 50 is not

  3. The nth term is 3n + 4. Which term is 34?

    The 10th term

  1. Find the hop. Write the times table. Find the gap. Write the nth term.

    5n + 2
    n1234+5+5+5171217223n2nth term =n+4

  2. Find the hop. Write the times table. Find the gap. Write the nth term.

    3n + 3
    n123416912153n2nth term =n+4

  3. Find the nth term of 9, 11, 13, 15, …

    nth term = 2n + 7
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