Geometric Sequences (Edexcel A-Level Mathematics): Quizzes

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Geometric Sequences
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What defines a geometric sequence?

A common ratio between consecutive terms

What is the formula for the nthn^{th} term of a geometric sequence?

un=arn−1u_n = ar^{n-1}

How do you find the common ratio in a geometric sequence?

Divide a term by its previous term

In the sequence 2,4,8,16,32,…2, 4, 8, 16, 32, \ldots, what is the first term aa?

a=2a = 2

For the sequence 100,50,25,12.5,…100, 50, 25, 12.5, \ldots, what is the common ratio rr?

r=12r = \frac{1}{2}

For 1,5,25,125,…1, 5, 25, 125, \ldots with un=5n−1u_n = 5^{n-1}, what is u3u_3?

2525

What is the formula for the sum of nn terms of a geometric sequence?

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

For the sequence 3,−12,48,−192,…3, -12, 48, -192, \ldots, what is the common ratio?

r=−4r = -4

If ar=0.5ar = 0.5 and ar4=32ar^4 = 32, what is r3r^3?

6464

To solve 4n−1<800004^{n-1} < 80000 for nn, which method is required?

Logarithms

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