Find the nth Term

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

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

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

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

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'.

Illustrative background for 2n+3 ?? "content

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’.

1Angles

1.17 Facts About Angles

1.1.1Facts About Angles

1.1.2More Facts About Angles

1.2Identify the Angle

1.2.1Identify the Angle

1.3Angles on a Straight Line

1.3.1Angles on a Straight Line

1.3.2Angles on a Straight Line - Practice Questions

1.4Angles in a Circle

1.4.1Angles in a Circle

1.5Angles in Triangles

1.5.1Angles in a Triangle

2Fractions

2.1Simplifying Fractions

2.1.1Simplifying Fractions

2.1.2Identifying Equivalent Fractions

2.2Improper Fractions & Mixed Numbers

2.2.1Improper Fractions & Mixed Numbers

2.2.2Converting Mixed Numbers to Improper Fractions

2.2.3Converting Improper Fractions to Mixed Numbers

2.3Fractions of Numbers

2.3.1Fractions of Numbers

2.4Expressing Shaded Areas as Fractions

2.4.1Expressing Shaded Areas as Fractions

3Time

3.112-Hour & 24-Hour Clocks

3.1.1Difference Between 12-Hour & 24-Hour Clocks

3.1.2Changing the 12-Hour Clock to the 24-Hour Clock

3.1.3Changing the 24-hour Clock to the 12-Hour Clock

3.2Time-Related Problems

3.2.1Time-Related Problems

3.2.2Timetable & Schedule Problems

4Prime Numbers

4.1Prime Numbers

4.1.1Prime Numbers

5Probability

5.1Probability

5.1.1Probability Scale

5.1.2Probability Fractions

5.1.3Experimental Probability

6Ratio

6.1Ratios

6.1.1Ratios

7Sequences

7.1Constant Sequences

7.1.1Constant Increase Sequences

7.1.2Constant Decrease Sequences

7.2Doubling & Halving Sequences

7.2.1Doubling Sequences

7.2.2Halving Sequences

7.3Alternating Patterns & Two-Step Sequences

7.3.1Alternating Pattern Sequences

7.4Two-Step Patterns

7.4.1Two-Step Patterns

7.5The nth Term

7.5.1Find the nth Term

7.5.2Using the nth Term

8Area & Perimeter

8.1Perimeter of a Quadrilateral

8.1.1Finding the Perimeter of a Quadrilateral

8.1.2Finding the Missing Length

8.2Area of a Quadrilateral

8.2.1Finding the Area of a Quadrilateral

8.2.2Finding the Missing Side of a Rectangle

8.2.3Finding the Missing Side of a Square

8.2.4Finding the Area of Irregular Shapes

8.3Area of a Triangle

8.3.1Finding the Area of a Triangle

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