- Tables, Graphs, Functions and Sequences
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- 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

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# Finding the next terms of an arithmetic sequence with whole numbers

A sequence is a set or series of numbers that follow a certain rule.

For example −

1, 3, 5, 7… is a sequence of numbers that follow a rule: To find a number in this sequence we add 2 to the previous number.

An Arithmetic sequence is a series of numbers where each number is found by adding or subtracting a constant from the previous number.

The constant in an arithmetic sequence is known as the common difference ‘d’.

In general, we write an arithmetic sequence as follows…

a, a + d, a + 2d , a + 3d, a + 4d…

where, a is the first term and d is the common difference.

**The rule for finding nth term of an arithmetic sequence**

a_{n} = a + (n−1)d

a_{n} is the n^{th} term, d is the common difference.

The first three terms of an arithmetic sequence are 13, 18, and 23. Find the next two terms of this sequence.

### Solution

**Step 1:**

Given the arithmetic sequence 13, 18 and 23. The common difference is

18 −13 = 23 −18 = 5 or d = 5

**Step 2:**

The next two terms in the sequence are 23 + 5 and 28 + 5 or 28 and 33

So the answer is 28 and 33

The first three terms of an arithmetic sequence are 11, 4, and −3. Find the next two terms of this sequence.

### Solution

**Step 1:**

Given the arithmetic sequence 11, 4 and −3. The common difference is

4 −11 = −3 − 4 = −7 or d = −7

**Step 2:**

The next two terms in the sequence are −3 −7 and −10 −7 or −10 and −17

So the answer is −10 and −17