Algebra II : Geometric Sequences
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Example Question #21 : Geometric Sequences
A sequence begins as follows:
Which statement is true?
The sequence may be geometric.
None of these
The sequence may be arithmetic and geometric.
The sequence may be arithmetic.
The sequence cannot be arithmetic or geometric.
The sequence may be geometric.
An arithmetic sequence is one in which each term is generated by adding the same number - the common difference - to the previous term. As can be seen here, the difference between each term and the previous term varies from term to term:
The sequence cannot be arithmetic.
A geometric sequence is one in which each term is generated by multiplying the previous term by the same number - the common ratio. As can be seen here, the ratio of each term to the previous one is the same:
The sequence could be geometric.
Example Question #22 : Geometric Sequences
Find the sum for the first 25 terms in the series
Before we add together the first 25 terms, we need to determine the structure of the series. We know the first term is 60. We can find the common ratio r by dividing the second term by the first:
We can use the formula 
The terms we are adding together are 
Common mistakes would involve order of operations - make sure you do exponents first, then subtract, then multiply/divide based on what is grouped together.
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