Geometric Sequences (Grade 12 NSC Matric Mathematics): Flashcards

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Geometric Sequences
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Definition: geometric sequence

Each term = previous term × constant ratio

Constant ratio (r) definition

Fixed number to multiply each term by for next term

Formula: constant ratio

r=TnTn−1r = \frac{T_n}{T_{n-1}}

General term formula

Tn=arn−1T_n = ar^{n-1}

Meaning of 'a' in Tn=arn−1T_n = ar^{n-1}

First term of the sequence

Why (n-1) power in general term formula

First term has power 0, so nth has power (n-1)

Test for geometric sequence

Check all consecutive ratios are equal

Geometric mean formula for a and b

x=±abx = \pm\sqrt{ab}

Geometric sequences grow by

Multiplication (not addition)

Valid geometric mean values

Both positive and negative

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