Edexcel IGCSE Maths 复习笔记 3.1.3 Arithmetic Sequences - Sum of n terms

Edexcel IGCSE Maths 复习笔记 3.1.3 Arithmetic Sequences - Sum of n terms

What is an arithmetic sequence or arithmetic series?

  • Ensure you are familiar with Sequences – Basics and Linear

 

3.1.3-ArSeqSum-Notes-fig1

 

  • An arithmetic sequence is a sequence of numbers that increase or decrease by the same amount from one term to the next
    • This amount is called the common difference
    • eg. 5, 9, 13, 17, 21, ...  common difference of 4
    • eg2. 24, 17, 10, 3, -4, ..., -95  common difference of -7

     

  • An arithmetic series is where terms are added together
    • eg. 5 + 9 + 13 + 17 + 21 + ...
    • eg2. 24 + 17 + 10 + 3 + -4 + ... + -95

     

 

3.1.3-ArSeqSum-Notes-fig2

 

 

  • Lots of letters are used in sequences, make sure you are familiar with them
    • a – the first term in an arithmetic series
    • d – the common difference of an arithmetic series
    • n – the number of terms in the arithmetic seriesSome series go on forever (ie.  have an infinite number of terms – but it could be that only the first 10 terms, say, are of interest, so n = 10)

     

  • Sn is used for the sum of the first n terms of an arithmetic series

How do I find the sum of an arithmetic series?

  • There is a formula for adding up the first n terms of an arithmetic series
    • The formula is included on the formulae sheet

     

 

3.1.3-ArSeqSum-Notes-fig3

 

  • You do not need to where the formula comes from but, just for fun, here’s a hint
    • To add up the numbers 1 to 10
    • Write out the numbers1 2 3 4 5 6 7 8 9 10
    • Write them backwards10 9 8 7 6 5 4 3 2 1
    • Add up both lists11  11  11  11  11  11  11  11  11 11
    • This is 10 × 11 = 110
    • But this is twice the sum as two lots were added together
    • So the sum of the numbers 1 to 10 is 110 ÷ 2 = 55

     

3.1.3-ArSeqSum-Notes-fig4

Exam Tip

It is not necessarily Sn you’ll be asked to find in a question – any of a, d, n and S could be asked for.To avoid confusion always write down what you know and what you are trying to find.Remember that substituting known values into a formula first, then rearranging, is easier than the other way round!

Worked Example

3.1.3-ArSeqSum-Example-fig1-sol

转载自savemyexam

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