Summing a Geometric Series (HSC SSCE Mathematics Advanced): Quizzes

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Summing a Geometric Series
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Which formula should be used for r>1r > 1?

Sn=a(rn−1)r−1S_n = \frac{a(r^n - 1)}{r - 1}

What key technique is used in deriving the GP sum formula?

Multiply by rr then subtract

For the series 2−6+18−⋯2 - 6 + 18 - \cdots, what are aa and rr?

a=2a = 2, r=−3r = -3

What is the sum of 50+51+⋯+575^0 + 5^1 + \cdots + 5^7?

97656

What is the sum of the first 6 terms of 2−6+18−⋯2 - 6 + 18 - \cdots?

-364

If S4=200S_4 = 200 and r=3r = 3, what is the first term aa?

5

When r=1r = 1, what is the sum formula?

Sn=anS_n = an

How many terms are in the series 50+51+⋯+575^0 + 5^1 + \cdots + 5^7?

8

For simpler problems, which method is often quicker to find nn?

Trial-and-error

Why choose a specific formula for r>1r > 1 vs r<1r < 1?

To avoid negative denominators

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Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

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The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

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