Edexcel IGCSE Maths 復習筆記 3.1.3 Arithmetic Sequences - Sum of n terms
Edexcel IGCSE Maths 復習筆記 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
- 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
- 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
- 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
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
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