7.5.1

Find the nth Term

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Finding the 'nth Term'

When you are asked to find the ‘nth term’, you are being asked to find a rule that can be used to find the value of any step in a particular sequence.

How to find the nth term

How to find the nth term

  • You need to find a rule that takes you from the step number to the corresponding number in the sequence.
    • So you need to find a rule that takes 1 to 5, 2 to 7, 3 to 9 and so on.
Work out the sequence difference

Work out the sequence difference

  • First, work out the difference between the numbers in the sequence. This tells you how much you need to multiply 'n' by.
Multiply by 2

Multiply by 2

  • The difference between the numbers in the sequence is 2.
    • So the first part of the rule is 'multiply by 2'.
Add 3

Add 3

  • Next, work out what you need to add or subtract to get the number in the sequence.
    • To get from 2 to 5, add 3. So the second part of the rule is 'add 3'.
2n+3

2n+3

  • In algebra, we write the rule 'multiply by 2 and add 3' as 2n + 3 (we do not use the multiplication sign). This is the ‘nth term’.
Jump to other topics
1

Angles

1.1

7 Facts About Angles

1.1.1Facts About Angles1.1.2More Facts About Angles
1.2

Identify the Angle

1.2.1Identify the Angle
1.3

Angles on a Straight Line

1.3.1Angles on a Straight Line1.3.2Angles on a Straight Line - Practice Questions
1.4

Angles in a Circle

1.4.1Angles in a Circle
1.5

Angles in Triangles

1.5.1Angles in a Triangle
2

Fractions

2.1

Simplifying Fractions

2.1.1Simplifying Fractions2.1.2Identifying Equivalent Fractions
2.2

Improper Fractions & Mixed Numbers

2.2.1Improper Fractions & Mixed Numbers2.2.2Converting Mixed Numbers to Improper Fractions2.2.3Converting Improper Fractions to Mixed Numbers
2.3

Fractions of Numbers

2.3.1Fractions of Numbers
2.4

Expressing Shaded Areas as Fractions

2.4.1Expressing Shaded Areas as Fractions
3

Time

3.1

12-Hour & 24-Hour Clocks

3.1.1Difference Between 12-Hour & 24-Hour Clocks3.1.2Changing the 12-Hour Clock to the 24-Hour Clock3.1.3Changing the 24-hour Clock to the 12-Hour Clock
3.2

Time-Related Problems

3.2.1Time-Related Problems3.2.2Timetable & Schedule Problems
4

Prime Numbers

4.1

Prime Numbers

4.1.1Prime Numbers
5

Probability

5.1

Probability

5.1.1Probability Scale5.1.2Probability Fractions5.1.3Experimental Probability
6

Ratio

6.1

Ratios

6.1.1Ratios
7

Sequences

7.1

Constant Sequences

7.1.1Constant Increase Sequences7.1.2Constant Decrease Sequences
7.2

Doubling & Halving Sequences

7.2.1Doubling Sequences7.2.2Halving Sequences
7.3

Alternating Patterns & Two-Step Sequences

7.3.1Alternating Pattern Sequences
7.4

Two-Step Patterns

7.4.1Two-Step Patterns
7.5

The nth Term

7.5.1Find the nth Term7.5.2Using the nth Term
8

Area & Perimeter

8.1

Perimeter of a Quadrilateral

8.1.1Finding the Perimeter of a Quadrilateral8.1.2Finding the Missing Length
8.2

Area of a Quadrilateral

8.2.1Finding the Area of a Quadrilateral8.2.2Finding the Missing Side of a Rectangle8.2.3Finding the Missing Side of a Square8.2.4Finding the Area of Irregular Shapes
8.3

Area of a Triangle

8.3.1Finding the Area of a Triangle

Practice questions on Find the nth Term

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    What's the second part of the nth term for this sequence?<br> 3, 11, 19, 27... <br><br>8n - ?Multiple choice
  2. 2
    What's the second part of the nth term for this sequence?<br> 17, 15, 13, 11 <br><br>-2n + ?Multiple choice
  3. 3
    What's the second part of the nth term for this sequence?<br> -11, -9, -7, -5 <br><br>2n - ?Multiple choice
  4. 4
    What's the nth term of this sequence?<br><br>4, 9, 14, 19...Multiple choice
  5. 5
    What's the nth term of this sequence?<br><br>-1, 5, 11, 17...Multiple choice
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Two-Step Patterns

Using the nth Term