Solving Problems Involving APs and GPs (HSC SSCE Mathematics Advanced): Flashcards

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Solving Problems Involving APs and GPs
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Condition for 3 numbers in AP

ba=cbb - a = c - b

Condition for 3 numbers in GP

ba=cb\frac{b}{a} = \frac{c}{b}

Alternative GP condition for 3 numbers

b2=acb^2 = ac

How to eliminate aa in AP simultaneous equations

Subtraction

How to eliminate aa in GP simultaneous equations

Division

General term formula for AP

Tn=a+(n1)dT_n = a + (n-1)d

General term formula for GP

Tn=arn1T_n = ar^{n-1}

When trial-and-error is practical for GP

Small target values, quick answer, calculator available

When logarithms are better for GP

Large values, exact solution, trial-and-error too long

Alternative AP condition for 3 numbers

2b=a+c2b = a + c

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