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GCSE Quadratic Sequences Questions and Answers

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Question 26 - AQA GCSE Higher Maths Past Paper 1 November 2021

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Question 20 - Edexcel GCSE Higher 2020 Past Paper 2 - Algebra,Sequences Questions By Topic

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Question 13 - AQA GCSE Foundation 2019 Past Paper 3 - Algebra, Quadratic Sequences, Questions By Topic

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Question 16 - Edexcel GCSE Higher 2018 Past Paper 3 - Algebra, Sequences, Quadratic Sequences Questions By Topic

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Quadratic Sequences for GCSE Maths

1. What are Quadratic Sequences?

Quadratic Sequences:

Quadratic sequences are ordered sets of numbers that follow a rule based on the sequence 

n² or the square numbers.

Quadratic sequences always include an n² term.

The resulting sequences don’t have a common difference between each term as linear sequences do, but rather the difference between the differences remains the same.

For example:

Sequence 6, 12, 22, 36

GCSE Quadratics Sequences Content Image 01

The difference of the sequence is not common. Let's check the second difference,

GCSE Quadratics Sequences Content Image 02

The second difference is common. Hence the expression will contain a 4n² term

Steps of finding nth term of Quadratic sequence 

Step 1: Find the difference between each pair of terms.

Step 2: The difference is changing, so work out the difference between the differences.

Step 3:Divide this value by 2-this gives the coefficient of the n² term (a)

Step 4: Subtract the n² term from each term in the sequence. This will give you a linear sequence.

Step 5: Find the rule for the nth term of the linear sequence and add this on to the n² term.

For example:

Find nth term of the sequence 4 11  20  31  44

GCSE Quadratics Sequences Content Image 03

2. Examples of Quadratic sequence

Example 1:

The first 5 terms of a quadratic sequence:

 4 10 18 28 40

Find an expression, in terms of n, for the nth term of this quadratic sequence.

Also find the next  two terms.

Solution:

GCSE Quadratics Sequences Content Image 03

Example 2:

A quadratic sequence has an nth of 2n²+3n-1 . workout the value of 6th term.

Solution:

GCSE Quadratics Sequences Content Image 04

Example 3:

A sequence has a nth term of n²-6n+7. Workout which term in the sequence has a value of 23.

Solution:

GCSE Quadratics Sequences Content Image 05

Quiz Questions
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GCSE Topics

  • Data Visualisation (4)
  • Algebra (1,176)
  • Ratio, Proportion and Rates of Change (443)
  • Geometry and Measures (809)
  • Statistics (274)
  • Probability (258)
  • Statistical Measures (5)
  • Numbers (1,084)
    • Frequently Asked Questions
    What are the main topics in GCSE Maths?

    The main topics in GCSE Maths are:

    • Numbers
    • Algebra 
    • Ratio, Proportion and Rates of Change 
    • Geometry and Measures
    • Statistics 
    • Probability 
    • Statistical Measures 
    • Data Visualisation 

    With regular practice of GCSE Maths topic-wise questions and GCSE Maths past pacers, you can easily score high marks.

    Is GCSE Maths hard?

    Although many people think of GCSE maths as a difficult subject, with the correct training and preparation,you can master it in time. You can practice GCSE Maths  topic-wise questions daily to improve speed, accuracy, and time and to score high marks in the GCSE Maths exam.

    What is a good grade on GCSE Maths Exam?

    A grade of 4 or 5 would be considered "good" because the government has established a 4 as the passing grade; a grade of 5 is seen as a strong pass. Therefore, anything that exceeds this level would be considered good. You can practice GCSE Maths topic-wise questions to score good grades in the GCSE Maths exam.

    How can I get full marks in GCSE Maths?

    You can get a high score in GCSE Maths through meticulous practice of GCSE Maths topic-wise questions and GCSE Maths past papers.

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