- 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 the next terms of a geometric sequence with whole numbers

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

For example −

2, 4, 6, 8… is a sequence of numbers that follow a rule −

A geometric sequence is a series of numbers where each number is found by multiplying the previous number by a constant.

The constant in a geometric sequence is known as the common ratio r.

In general, we write a geometric sequence as follows…

a, ar, ar^{2}, ar^{3}, ar^{4}…

where, a is the first term and r is the common ratio.

**The rule for finding nth term of a geometric sequence**

a_{n} = ar^{n−1}

a_{n} is the n^{th} term, r is the common ratio.

The first three terms of a geometric sequence are 6, -24, and 96. Find the next two terms of this sequence.

### Solution

**Step 1:**

The geometric sequence given is 6, −24, 96…

The common ratio is $\frac{-24}{6}$ = $\frac{96}{-24}$ = −4

**Step 2:**

The next two terms of the sequence are −

96(−4) = −384; −384(−4) = 1536.

So the terms are −384 and 1536

The first three terms of a geometric sequence are 4, 16, and 64. Find the next two terms of this sequence.

### Solution

**Step 1:**

The geometric sequence given is 4, 16, 64…

The common ratio is $\frac{16}{4}$ = $\frac{64}{16}$ = 4

**Step 2:**

The next two terms of the sequence are −

64 × 4 = 256; 256 × 4 = 1024.

So the terms are 256 and 1024