Pattern and Function

A pattern uses the following sequence: $5, 10, 15, 20, \dots$. What is the 6th term in this sequence?

What is the missing value in the input-output table if the rule is $y = x - 2$?

Which number pattern follows the rule 'Multiply by 2'?

In the function machine shown, if the output is $15$, what was the input?

A pattern is shown using circles. Each step adds the same number of circles to the previous step. Looking at the diagram, how many circles will be in Step 5?

If the pattern of rectangles follows the sequence $3, 7, 11, 15, \dots$, what is the 10th number?

Find the missing number in the table. The relationship is $y = 3x + 1$.

A gardener is planting flowers in a triangular pattern for a community garden. In the first row, there are 3 flowers. In the second row, there are 7 flowers. In the third row, there are 11 flowers. If the gardener continues this pattern of adding the same number of flowers to each new row, how many flowers will be in the 6th row?

A baker makes cupcakes in a sequence. Monday: 12 cupcakes; Tuesday: 24 cupcakes; Wednesday: 36 cupcakes. If she continues this pattern of adding 12 more each day, how many cupcakes will she have made in total by the end of Friday?

A cooling machine reduces the temperature of a liquid by $4^{\circ}C$ every 10 minutes. If the starting temperature is $80^{\circ}C$, what will the temperature be after 50 minutes?

A student is making a pattern using triangles. Look at the flow of the pattern shown below. If the rule is to 'add 3' to find the next number of triangles, what is the value of the missing number?

A student saves money in a piggy bank. On Monday she saves $1$ dollar, Tuesday $2$ dollars, Wednesday $3$ dollars. If she follows this pattern, how much does she save on Saturday?

Which number comes next in the pattern? $2, 4, 8, 16, \dots$

A fence is made by placing posts $2$ meters apart. If there are $5$ posts in a straight line, how many $2$-meter gaps are there?

A pattern is created by repeating a specific shape. In this geometry pattern, the student starts at $x=1$ and moves to the next point by doubling the distance from the bottom line ($y=0$). Based on the points plotted on the graph, what is the value of the rule for the next $y$ coordinate when $x=4$?

Look at the coordinate plane. The line shows the relationship between $x$ and $y$. What is the $y$ value when $x = 3$?

Find the rule that links the input to the output: Input: $2, 4, 6, 8$ Output: $1, 2, 3, 4$

A fence is built using posts and rails. 2 posts need 3 rails. 3 posts need 6 rails. 4 posts need 9 rails. If the pattern continues, how many rails are needed for 12 posts?

An elevator starts on the ground floor (Floor 0). It goes up 4 floors, then down 2 floors, then up 4 floors, then down 2 floors. If this pattern of movement (Up 4, Down 2) continues, which floor will the elevator be on after the 10th movement?

A geometric pattern uses squares. Figure 1 is a $1 \times 1$ square. Figure 2 is a $3 \times 3$ square with the center $1 \times 1$ removed. Figure 3 is a $5 \times 5$ square with the center $3 \times 3$ removed. How many unit squares are in Figure 5?

A 'Number Machine' follows a specific rule to change an 'In' number into an 'Out' number. Based on the diagram, if the number 10 is put into the machine, what number will come out?

A student is creating a pattern of squares. In each step, the total number of squares grows. Following the rule shown in the diagram, how many squares will be in Step 4?

What is the next shape in this rotating pattern?

If one star equals $3$ points, how many points do $4$ stars equal?

If the rule is $y = 10 - x$, what is $y$ when $x = 3$?

Look at the pattern of tiles. How many white tiles will surround a $3 \times 3$ block of gray tiles?

Which coordinate pair follows the rule $y = x + 4$?

A string of lights has a pattern of colors: Red, Blue, Green, Yellow, Red, Blue, Green, Yellow... If this pattern continues, what will be the color of the $35^{th}$ light?

Sarah is saving money for a bike. She starts with $50. Every week she adds$15. Which function $S(w)$ represents the total amount of money Sarah has after $w$ weeks?

A water tank is leaking. At 1:00 PM, it has $500$ liters. At 2:00 PM, it has $475$ liters. At 3:00 PM, it has $450$ liters. If the leak continues at this rate, at what time will the tank have $350$ liters left?