Source: https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-5-1-find-the-nth-term [Revision notes](https://senecalearning.com/en-gb/revision-notes.md) › [11+](https://senecalearning.com/en-gb/revision-notes/11.md) › [Maths](https://senecalearning.com/en-gb/revision-notes/11/maths.md) › [11+ Maths](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths.md) › Find the nth Term # Find the nth Term 11+ Maths, topic 7.5.1 ## 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](https://image-v2.cdn.app.senecalearning.com/2019-06/0af975fc-d359-4f54-a273-20b713ced589/Nth-Term-Table-%20(2).png) - 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](https://image-v2.cdn.app.senecalearning.com/2019-06/4e930496-4249-40dd-b0c5-2c3929e4e009/Nth-Term-Table-%2B2.png) - 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](https://image-v2.cdn.app.senecalearning.com/2019-06/9d572939-211f-4d59-a473-5565c5ab32da/Nth-Term-Table-x2%20(6).png) - 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](https://image-v2.cdn.app.senecalearning.com/2019-06/f30322fb-2e2a-47a4-8afe-3d468bb73205/Nth-Term-Table-x2%20(8).png) - 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](https://image-v2.cdn.app.senecalearning.com/2019-06/d048f41a-d3a7-475f-8cc7-cfb2d463362c/Nth-Term-Table-x2%20(11).png) - 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’. ## Test yourself on Find the nth Term - What's the second part of the nth term for this sequence? 3, 11, 19, 27... 8n - ? - What's the second part of the nth term for this sequence? 17, 15, 13, 11 -2n + ? - What's the second part of the nth term for this sequence? -11, -9, -7, -5 2n - ? - What's the nth term of this sequence?4, 9, 14, 19... - What's the nth term of this sequence?-1, 5, 11, 17... [Practise this topic for free](https://app.senecalearning.com/classroom/course/f4a9de91-3dcc-4e19-b180-1286357dded5/section/54def990-4512-44d4-8bda-d469c3b83076/session) - Previous topic: [7.4.1 Two-Step Patterns](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-4-1-two-step-patterns.md) - Next topic: [7.5.2 Using the nth Term](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-5-2-using-the-nth-term.md) ## 11+ Maths contents ### 1 Angles - 1.1 7 Facts About Angles - [1.1.1 Facts About Angles](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/1-1-1-facts-about-angles.md) - [1.1.2 More Facts About Angles](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/1-1-2-more-facts-about-angles.md) - 1.2 Identify the Angle - [1.2.1 Identify the Angle](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/1-2-1-identify-the-angle.md) - 1.3 Angles on a Straight Line - [1.3.1 Angles on a Straight Line](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/1-3-1-angles-on-a-straight-line.md) - [1.3.2 Angles on a Straight Line - Practice Questions](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/1-3-2-angles-on-a-straight-line-practice-questions.md) - 1.4 Angles in a Circle - [1.4.1 Angles in a Circle](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/1-4-1-angles-in-a-circle.md) - 1.5 Angles in Triangles - [1.5.1 Angles in a Triangle](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/1-5-1-angles-in-a-triangle.md) ### 2 Fractions - 2.1 Simplifying Fractions - [2.1.1 Simplifying Fractions](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-1-1-simplifying-fractions.md) - [2.1.2 Identifying Equivalent Fractions](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-1-2-identifying-equivalent-fractions.md) - 2.2 Improper Fractions & Mixed Numbers - [2.2.1 Improper Fractions & Mixed Numbers](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-2-1-improper-fractions-and-mixed-numbers.md) - [2.2.2 Converting Mixed Numbers to Improper Fractions](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-2-2-converting-mixed-numbers-to-improper-fractions.md) - [2.2.3 Converting Improper Fractions to Mixed Numbers](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-2-3-converting-improper-fractions-to-mixed-numbers.md) - 2.3 Fractions of Numbers - [2.3.1 Fractions of Numbers](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-3-1-fractions-of-numbers.md) - 2.4 Expressing Shaded Areas as Fractions - [2.4.1 Expressing Shaded Areas as Fractions](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-4-1-expressing-shaded-areas-as-fractions.md) ### 3 Time - 3.1 12-Hour & 24-Hour Clocks - [3.1.1 Difference Between 12-Hour & 24-Hour Clocks](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/3-1-1-difference-between-12-hour-and-24-hour-clocks.md) - [3.1.2 Changing the 12-Hour Clock to the 24-Hour Clock](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/3-1-2-changing-the-12-hour-clock-to-the-24-hour-clock.md) - [3.1.3 Changing the 24-hour Clock to the 12-Hour Clock](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/3-1-3-changing-the-24-hour-clock-to-the-12-hour-clock.md) - 3.2 Time-Related Problems - [3.2.1 Time-Related Problems](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/3-2-1-time-related-problems.md) - [3.2.2 Timetable & Schedule Problems](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/3-2-2-timetable-and-schedule-problems.md) ### 4 Prime Numbers - 4.1 Prime Numbers - [4.1.1 Prime Numbers](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/4-1-1-prime-numbers.md) ### 5 Probability - 5.1 Probability - [5.1.1 Probability Scale](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/5-1-1-probability-scale.md) - [5.1.2 Probability Fractions](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/5-1-2-probability-fractions.md) - [5.1.3 Experimental Probability](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/5-1-3-experimental-probability.md) ### 6 Ratio - 6.1 Ratios - [6.1.1 Ratios](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/6-1-1-ratios.md) ### 7 Sequences - 7.1 Constant Sequences - [7.1.1 Constant Increase Sequences](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-1-1-constant-increase-sequences.md) - [7.1.2 Constant Decrease Sequences](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-1-2-constant-decrease-sequences.md) - 7.2 Doubling & Halving Sequences - [7.2.1 Doubling Sequences](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-2-1-doubling-sequences.md) - [7.2.2 Halving Sequences](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-2-2-halving-sequences.md) - 7.3 Alternating Patterns & Two-Step Sequences - [7.3.1 Alternating Pattern Sequences](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-3-1-alternating-pattern-sequences.md) - 7.4 Two-Step Patterns - [7.4.1 Two-Step Patterns](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-4-1-two-step-patterns.md) - 7.5 The nth Term - [7.5.1 Find the nth Term](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-5-1-find-the-nth-term.md) - [7.5.2 Using the nth Term](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-5-2-using-the-nth-term.md) ### 8 Area & Perimeter - 8.1 Perimeter of a Quadrilateral - [8.1.1 Finding the Perimeter of a Quadrilateral](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/8-1-1-finding-the-perimeter-of-a-quadrilateral.md) - [8.1.2 Finding the Missing Length](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/8-1-2-finding-the-missing-length.md) - 8.2 Area of a Quadrilateral - [8.2.1 Finding the Area of a Quadrilateral](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/8-2-1-finding-the-area-of-a-quadrilateral.md) - [8.2.2 Finding the Missing Side of a Rectangle](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/8-2-2-finding-the-missing-side-of-a-rectangle.md) - [8.2.3 Finding the Missing Side of a Square](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/8-2-3-finding-the-missing-side-of-a-square.md) - [8.2.4 Finding the Area of Irregular Shapes](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/8-2-4-finding-the-area-of-irregular-shapes.md) - 8.3 Area of a Triangle - [8.3.1 Finding the Area of a Triangle](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/8-3-1-finding-the-area-of-a-triangle.md)