Finding Term n in a Sequence Modelling Geometric Growth and Decay (VCE SSCE General Mathematics): Flashcards

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Finding Term n in a Sequence Modelling Geometric Growth and Decay
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General formula for nth term of geometric sequence

Vn=Rn×V0V_n = R^n \times V_0

Condition for geometric growth (value increases)

R>1R > 1

Condition for geometric decay (value decreases)

R<1R < 1

Compound interest formula

Vn=(1+r100)n×V0V_n = \left(1 + \frac{r}{100}\right)^n \times V_0

Reducing-balance depreciation formula

Vn=(1r100)n×V0V_n = \left(1 - \frac{r}{100}\right)^n \times V_0

Credit card daily compounding formula

A=P(1+r36500)nA = P\left(1 + \frac{r}{36500}\right)^n

Why 36,500 in credit card formula denominator

365 days × 100 for percentage conversion

Formula for total interest earned

Interest=VnV0\text{Interest} = V_n - V_0

Effect of more frequent compounding on final value

Higher final value (interest calculated more often)

Definition of inflation

Continuous upward movement in general level of prices

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