Geometric Sequences & Series (AQA A-Level Mathematics): Quizzes

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Geometric Series
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What term describes a geometric series where the sum approaches infinity as n→∞n \rightarrow \infty?

Diverges

What term describes a geometric series where the sum approaches a finite value as n→∞n \rightarrow \infty?

Converges

For a geometric series to converge, what condition must the common ratio rr satisfy?

∣r∣<1|r| < 1

What is the formula for the sum to infinity of a converging geometric series?

S∞=a1−rS_{\infty} = \frac{a}{1-r}

What happens to rnr^n as n→∞n \rightarrow \infty when ∣r∣<1|r| < 1?

rn→0r^n \rightarrow 0

Find S∞S_{\infty} for the series 6+2+23+29+…6 + 2 + \frac{2}{3} + \frac{2}{9} + \ldots

99

Does the geometric series with common ratio r=34r = \frac{3}{4} converge or diverge?

Converges

If S∞=4aS_{\infty} = 4a in a geometric progression, what is the common ratio rr?

34\frac{3}{4}

If r=34r = \frac{3}{4} and the third term is 99, find the first term aa.

1616

Which series diverges according to the note's examples?

1+2+4+8+16+…1 + 2 + 4 + 8 + 16 + \ldots

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