An Introduction to Geometric Sequences (VCE SSCE General Mathematics): Flashcards

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An Introduction to Geometric Sequences
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Geometric sequence definition

Each term = previous term × fixed number (common ratio)

Common ratio (RR) in geometric sequence

Fixed multiplier connecting one term to the next

Formula for common ratio RR

R=any termprevious termR = \frac{\text{any term}}{\text{previous term}}

Arithmetic vs geometric sequences difference

Arithmetic: add/subtract; Geometric: multiply

Sequence behaviour when R>1R > 1

Increasing (exponential growth)

Sequence behaviour when 0<R<10 < R < 1

Decreasing towards zero (exponential decay)

How to verify a sequence is geometric

Check all consecutive term ratios are equal

Shape of geometric sequence graphs

Curves, not straight lines

Recursion in geometric sequences

Repeating multiplication process

Common ratio property throughout sequence

Remains constant

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