C2 Chapter 7: Geometric Series Dr J Frost

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C2 Chapter 7: Geometric Series Dr J Frost

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C2 Chapter 7: Geometric Series Dr J Frost (jfrosttiffin.kingston.sch.uk) www.drfrostmaths.com Last modified: 4th April 2016 2, 5, 8, 11, 14, 3 3 3 This is a: Arithmetic Series ? Geometric Series ? 3, 6, 12, 24, 48, ? ? 1 2 3 4 5 6 7

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C2 Chapter 7: Geometric Series Dr J Frost (jfrost@tiffin.kingston.sch.uk)
www.drfrostmaths.com Last modified: 4th April 2016

2, 5, 8, 11, 14, … +3 +3 +3 This is a: Arithmetic Series ? Geometric Series ? 3, 6, 12, 24, 48, … ? ?

1 2 3 4 5 6 7 ? ? ? ? ? ? ?

May 2013 (Retracted) Hint for (a): the common ratio between the first and second terms, and the second and third terms, is the same. a b ? ?

Arithmetic Series Geometric Series Determine the following: 3, 6, 12, 24, … 40, -20, 10, -5, … ? ? ? ? ?

?

The second term of a geometric sequence is 4 and the 4th term is 8.
The common ratio is positive. Find the exact values of:
The common ratio.
The first term.
The 10th term. ?

?

Edexcel June 2010 ? ? ? ? ?

Arithmetic Series Geometric Series ? ? Technically you could be asked in an exam the proof of the sum of a geometric series (it once came up!)
So let’s prove it…

Geometric Series Find the sum of the first 10 terms. ? ? ? ? ? ? ? ?

? ? ? ?

? ?

1 2 4 5 6 ? ? ? ? ? ? ? ? ? ?

1 + 2 + 4 + 8 + 16 + ... What can you say about the sum of each series up to infinity? 1 + 2 + 3 + 4 + 5 + ... 1 + 0.5 + 0.25 + 0.125 + ... This is divergent – the sum of the values tends towards infinity. This is convergent – the sum of the values tends towards a fixed value, in this case 2. This is divergent . This is known as the Harmonic Series Just for fun... ? ? ? ? ?

? ?

? ? ? ? ? ? ? ? ? ? ? ?

? ?

Edexcel May 2011 ? ? ? ?

Exercise 7D Q6, 7
Exercise 7E Q8
Exercise 7F Q10

C2 Chapter 7: Geometric Series Dr J Frost

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