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Edexcel GCSE Maths Quadratic sequences

Quadratic sequences

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A quadratic sequence is an ordered list of n numbers in which the difference in the first difference between consecutive terms, that is the second difference between terms, is constant. Therefore, a quadratic sequence can be described by formula:

Basics of quadratic sequences

The term to term rule of a quadratic sequence describes how to get from one term to the next in the sequence. To find the term to term rule, identify the common second difference term between consecutive terms. From the term to term rule and the first term of the sequence the position to term rule, or general rule, of a quadratic sequence can be worked out with the formula:

Generating terms in quadratic sequences

The general rule of a quadratic sequence can be used to work out the nth term of the sequence, the term at position n, and is given by the formula:

nth term of quadratic sequences

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Can the sequence {Un} = {4, 14, 40, 88, 164, …, Un} be called a quadratic sequence?

Edexcel GCSE Maths Quadratic sequences Can the sequence {Un} = {4, 14, 40, 88, 164, …, Un} be called a quadratic sequence?
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2

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Given the first three terms of a quadratic sequence are {3, 13, 27}, find the second common difference term.

Edexcel GCSE Maths Quadratic sequences Given the first three terms of a quadratic sequence are {3, 13, 27}, find the second common difference term.
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3

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Given the sequence {2, 8, 18, 32, 50, …, Un}, describe what is common between its terms.

Edexcel GCSE Maths Quadratic sequences Given the sequence {2, 8, 18, 32, 50, …, Un}, describe what is common between its terms.
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4

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Given the quadratic sequence {Un} = {βˆ’10, βˆ’14, βˆ’10, 2, 22, …, Un}, calculate the eighth term of the sequence.

Edexcel GCSE Maths Quadratic sequences Given the quadratic sequence {Un} = {βˆ’10, βˆ’14, βˆ’10, 2, 22, …, Un}, calculate the eighth term of the sequence.
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5

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Find the next term in the sequence in the quadratic sequence {3, 12, 27, 48, 75}.

Edexcel GCSE Maths Quadratic sequences Find the next term in the sequence in the quadratic sequence {3, 12, 27, 48, 75}.
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6

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Find the nth term, or general rule, of the sequence {Un} = {βˆ’9, βˆ’6, βˆ’1, 6, 15, …, Un}.

Edexcel GCSE Maths Quadratic sequences Find the nth term, or general rule, of the sequence {Un} = {βˆ’9, βˆ’6, βˆ’1, 6, 15, …, Un}.
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7

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Compute the first five terms of the sequence Un = nΒ² + 27n βˆ’ 184.

Edexcel GCSE Maths Quadratic sequences Compute the first five terms of the sequence Un = nΒ² + 27n βˆ’ 184.
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8

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Daley works at a charity shop on the weekends staring at 9:00 in the morning. On Saturday he sold 2 shirts in his first hour working, 5 shirts in his second, 10 in his third, and 17 in his fourth. On Sunday he sold twice the number of shirts in each hour. Find the nth term of the sequence of shirts Daley sold on Sunday.

Edexcel GCSE Maths Quadratic sequences Daley works at a charity shop on the weekends staring at 9:00 in the morning. On Saturday he sold 2 shirts in his first hour working, 5 shirts in his second, 10 in his third, and 17 in his fourth. On Sunday he sold twice the number of shirts in each hour. Find the nth term of the sequence of shirts Daley sold on Sunday.
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