
- 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
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, ar2, ar3, ar4…
where, a is the first term and r is the common ratio.
The rule for finding nth term of a geometric sequence
an = arn−1
an is the nth 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