Algebra, NAPX-H4-NC24

Question

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Worked Solution

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Variant 0

DifficultyLevel

702

Question

Herb made a number pattern using this rule:

next number = previous number × −-

and are whole numbers.


His number pattern is:

4,3,1,−3,−114, 3, 1, −3, −11


What is the next number in Herb's pattern?

Worked Solution

Using the rule and first 3 terms:

Let  x\ \large x = and  y\ \large y =


3=4x3=4\large x − y\large y … (1)

1=3x1=3\large x − y\large y … (2)

Subtract (1) −− (2),

x\large x = 2


Substitute x = 2 into (1)

y\large y = 5
∴ Next number = −11×2 − 5−11×2\ −\ 5
= −27-27

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Herb made a number pattern using this rule:
next number = previous number × ![](https://teacher.smartermaths.com.au/wp-content/uploads/2018/05/NAPX-H4-NC24_4.svg) $-$ ![](https://teacher.smartermaths.com.au/wp-content/uploads/2018/05/NAPX-H4-NC24_3.svg) ![](https://teacher.smartermaths.com.au/wp-content/uploads/2018/05/NAPX-H4-NC24_4.svg) and ![](https://teacher.smartermaths.com.au/wp-content/uploads/2018/05/NAPX-H4-NC24_3.svg) are whole numbers.

His number pattern is: > > $4, 3, 1, −3, −11$
What is the next number in Herb's pattern?
workedSolution
Using the rule and first 3 terms: Let $\ \large x$ = ![](https://teacher.smartermaths.com.au/wp-content/uploads/2018/05/NAPX-H4-NC24_4.svg) and $\ \large y$ = ![](https://teacher.smartermaths.com.au/wp-content/uploads/2018/05/NAPX-H4-NC24_3.svg)

$3=4\large x$ − $\large y$ … (1) $1=3\large x$ − $\large y$ … (2) Subtract (1) $−$ (2), > > $\large x$ = 2
Substitute x = 2 into (1) > > $\large y$ = 5
| | | | ----------- | ---------------------- | | ∴ Next number | \= $−11×2\ −\ 5$ | | | \= {{{correctAnswer}}} |
correctAnswer
$-27$

Answers

Is Correct?Answer
x

−19-19

x

−21-21

✓

−27-27

x

−29-29

Variant 1

DifficultyLevel

700

Question

Jen made a number pattern using this rule:

next number = previous number × −-

and are whole numbers.


Her number pattern is:

2,1,−2,−112, 1, -2, −11


What is the next number in Jen's pattern?

Worked Solution

Using the rule and first 3 terms:

Let  x\ \large x = and  y\ \large y =


1=2x1=2\large x − y\large y … (1)

−2=1x-2=1\large x − y\large y … (2)

Subtract (1) −− (2),

x\large x = 3


Substitute x = 3 into (1)

y\large y = 5
∴ Next number = −11×3 − 5−11×3\ −\ 5
= −38-38

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Jen made a number pattern using this rule:
next number = previous number × ![](https://teacher.smartermaths.com.au/wp-content/uploads/2018/05/NAPX-H4-NC24_4.svg) $-$ ![](https://teacher.smartermaths.com.au/wp-content/uploads/2018/05/NAPX-H4-NC24_3.svg) ![](https://teacher.smartermaths.com.au/wp-content/uploads/2018/05/NAPX-H4-NC24_4.svg) and ![](https://teacher.smartermaths.com.au/wp-content/uploads/2018/05/NAPX-H4-NC24_3.svg) are whole numbers.

Her number pattern is: > > $2, 1, -2, −11$
What is the next number in Jen's pattern?
workedSolution
Using the rule and first 3 terms: Let $\ \large x$ = ![](https://teacher.smartermaths.com.au/wp-content/uploads/2018/05/NAPX-H4-NC24_4.svg) and $\ \large y$ = ![](https://teacher.smartermaths.com.au/wp-content/uploads/2018/05/NAPX-H4-NC24_3.svg)

$1=2\large x$ − $\large y$ … (1) $-2=1\large x$ − $\large y$ … (2) Subtract (1) $−$ (2), > > $\large x$ = 3
Substitute x = 3 into (1) > > $\large y$ = 5
| | | | ----------- | ---------------------- | | ∴ Next number | \= $−11×3\ −\ 5$ | | | \= {{{correctAnswer}}} |
correctAnswer
$-38$

Answers

Is Correct?Answer
✓

−38-38

x

−27-27

x

−23-23

x

−20-20

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