 # Rules for describing sequences

Lesson

We have already looked at how to use algebra to describe number patterns, but we can also describe patterns in shapes and geometry in a similar way.

Let's have a look at a common pattern: We can use a table to more easily understand the pattern:

 Flowers ($x$x) $1$1 $2$2 $3$3 $4$4 Petals ($y$y) $5$5 $10$10 $15$15 $20$20

In this pattern, $x$x represents the step we are at (that is, the number of flowers) and $y$y represents the total number of petals at that step.

Notice that $y$y is increasing by $5$5 each time - in particular, the value of $y$y is always equal to $5$5 times the value of $x$x. We can express this as the algebraic rule $y=5x$y=5x.

Now that we have this rule, we can use it to predict future results. For example, if we wanted to know the total number of petals when there were $10$10 flowers, we have that $x=10$x=10 and so $y=5\times10=50$y=5×10=50 petals.

#### Worked Examples

##### Question 1

Use the rule to complete the table of values:

"The starting number is doubled, then $4$4 is subtracted."

1.  Starting Number ($N$N) $12$12 $13$13 $14$14 $15$15 Answer ($A$A) $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
2. Which of these equations describes the rule above?

$A=2\times\left(N-4\right)$A=2×(N4)

A

$A=N\times2-4$A=N×24

B

$A=N^2-4$A=N24

C

$A=2+N-4$A=2+N4

D

##### Question 2

a) Complete the table of values for the pattern shown

b) Write an algebraic rule for the relationship

c) Plot the graph of the line on the plane

##### Question 3

Matches were used to create the pattern pictured,

a) Complete the table of values

b) Write a formula that describes the relationship between the number of matches, $m$m, and the number of triangles, $t$t.

c) How many matches are required to make $53$53 triangles using this pattern?