Arithmetic & Geometric Sequences

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Presentation transcript:

Arithmetic & Geometric Sequences AS Maths with Liz Core 2

RECAP – Arithmetic Sequences

Arithmetic Sequences June 2012 – Question 1

Working out Use subtraction to find out how much the series is increasing by each time. Double check that this value is consistent as you progress through the series. The common difference is 9.

Working out Use the formula for finding the nth term… Use the formula for finding the sum to n terms…

Arithmetic Sequences tends to infinity June 2009 – Question 3

Working out Substitute in given information and solve for k.

Working out We know that k = 0.75, so substitute into given formula and find 3rd and 4th term.

Working out (i) To find L, simply replace and with L in your given equation. (ii) Solve for L.

Geometric Sequences

Example 1 Solution: Use given formulae to work out the 5th term, but for this, we need to find the common ratio r and the first term a. What do we multiply by to get from one term to the next? What is the first term? Formula to find the 5th term: Formula to find the sum to 10 terms:

Geometric Series Sum to Infinity In cases where the common ratio is between really small (a number between -1 and 1), the sum of the series will eventually converge on a certain value. Try the following using our formula from the previous slide…. Find As you can see, the more terms we add on, the less and less the sum changes. It seems to be approaching 0.4. Let’s skip to adding up the first 100 terms and see… Shortcut formula if common ration is between -1 and 1:

You try! June 2013 – Question 1

Working out

June 2013 - Question 7

Independent Study Announcement DUE 21ST APRIL Finish all exam questions from handout & mark in a colourful pen mymaths – Geometric Sequences mymaths – Binomial Expansion FULLY COMPLETE Core 2 June 2012 past paper. Mark in a colourful pen. This will be turned in. DUE 21ST APRIL Announcement Test over ARITHMETIC AND GEOMETRIC SEQUENCES will be held on 21st April. If your score has improved on arithmetic sequences, I will replace your existing grade.