Geometric Sequences
Key points
- Geometric Sequences are lists of numbers in which the previous term is multiplied by a constant to find the next term.
- Use the formula for geometric sequences to find any number in the sequence or to solve for unknown values.
Geometric Sequences are sequential lists of terms in which you multiply by a constant to find the next term. An example of an geometric sequence is seen to the right.
- In this example, the first term is 5, and it is being multiplied by 4 each time.
- In this case, 4 is a constant, or the common ratio.
- The common ratio can be either positive or negative.
- If the common ratio has a value of less than 1, then you are dividing to find the next term.
Formula Booklet
The key variables of a geometric sequence are the first term (u1) , the common ratio (r) , and the number of terms (n). They are shown in the formula to the left.
- This formula is used to find any number in the sequence (un), commonly known as the nth term.
- Find the common ratio by dividing any two consecutive numbers, using the later number in the sequence as the numerator.
Apart from this formula, geometric sequences can be generally expressed with the model shown to the right.
- This models the initial term being multiplied by the common ratio multiple times.
- This multiplication being repeated results in the exponents.
Not in Formula Booklet but important
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