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# Sequences and Series Help (page 2)

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Updated on Oct 27, 2011

### General Formula for Geometric Sequences

The generic formula for a geometric sequence is Term n = a1 × rn – 1, where n is the term you are looking for, a1 is the first term in the series, and r is the ratio that the sequence increases by. In the preceding example, n = 30 (the 30th term), a1 = 2 (because 2 is the first term in the sequence), and r = 2 (because the sequence increases by a ratio of 2; each term is two times the previous term).

You can use the formula Term n = a1 × rn – 1 when determining a term in any geometric sequence.

## Combination Sequences

Some sequences are defined by rules that are a combination of operations. The terms in these sequences do not differ by a constant value or ratio. For example, each number in a sequence could be generated by the rule "double the previous term and add one":

5, 11, 23, 47, 95, …

Each term in the following sequence is one less than four times the previous term. What is the next term in the sequence?

1, 3, 11, 43, …

Take the last given term in the sequence, 43, and apply the rule:

4(43) – 1 = 172 – 1 = 171

Find practice problems and solutions for these concepts at Sequences and Series Practice Problems.

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