- Tables, Graphs, Functions and Sequences
- Home
- Making a table and plotting points given a unit rate
- Graphing whole number functions
- Function tables with two-step rules
- Writing a function rule given a table of ordered pairs: One-step rules
- Graphing a line in quadrant 1
- Interpreting a line graph
- Finding outputs of a one-step function that models a real-world situation
- Finding outputs of a two-step function with decimals that models a real-world situation
- Writing and evaluating a function that models a real-world situation: Basic
- Graphing ordered pairs and writing an equation from a table of values in context
- Writing an equation and drawing its graph to model a real-world situation: Basic
- Identifying independent and dependent quantities from tables and graphs
- Finding the next terms of an arithmetic sequence with whole numbers
- Finding the next terms of a geometric sequence with whole numbers
- Finding patterns in shapes

# Finding patterns in shapes

In this lesson, we solve problems having series of shapes following some pattern.

We study and analyze the series of shapes to find the pattern or rule and based on that rule, we find the next or missing shape in the series.

The sequence of 3 figures shows a pattern. If the pattern repeats, how many marbles will there be in figure 5?

### Solution

**Step 1:**

In the given pattern above, horizontal marbles are always 3 in number and vertical marbles in numbers are 1, 2, 3

**Step 2:**

So, figure 5 will have 3 horizontal marbles and 5 vertical marbles. A total of 3 + 5 = 8 marbles.

The sequence of figures shows a pattern. If the pattern repeats, how many bubbles will Stage 6 have?

### Solution

**Step 1:**

The number of bubbles in the three stages are 1, 2, and 3. This is an arithmetic sequence whose common difference is 1.

**Step 2:**

As per the pattern, the stage 6 should have 3 + 1 + 1 + 1 or 6 bubbles.