How to find the missing term in a geometric sequence?
Understand the Problem
The question is asking how to determine the missing term in a geometric sequence, which typically involves finding a common ratio and applying it to the terms in the sequence.
Answer
To find a missing term in a geometric sequence, use the formula $c = b \cdot r$, where $r$ is the common ratio.
Answer for screen readers
The final answer will depend on the specific values in your geometric sequence.
Steps to Solve
- Identify the given terms of the geometric sequence
First, write down the terms of the geometric sequence that you're given. For example, if the sequence is: $$ a, b, c $$
- Determine the common ratio
To find the common ratio $r$, divide any term by the previous term. For instance, if $a$, $b$, and $c$ are consecutive terms: $$ r = \frac{b}{a} $$ or $$ r = \frac{c}{b} $$
- Use the common ratio to find the missing term
If you have a sequence with a missing term, say $a$, $b$, and a missing $c$, you can express $c$ in terms of $a$ and $r$: $$ c = b \cdot r $$
- Substitute known values
Insert the values you know into the equation to solve for the missing term. For example: $$ c = b \cdot \frac{b}{a} $$
- Calculate the missing term
Carry out the multiplication or division to find the missing term.
The final answer will depend on the specific values in your geometric sequence.
More Information
Geometric sequences are sequences where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. Understanding this can help you quickly find missing terms.
Tips
- Forgetting to check that the ratio is constant.
- Mixing up the order of terms when calculating the common ratio.
- Not applying the common ratio correctly when calculating the missing term.
