Sequences and Series Arithmetic series..

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Presentation transcript:

Sequences and Series Arithmetic series.

Sequence Series List with commas. Indicated sum, addition of terms. 3, 8, 13, 18 3 + 8 + 13 + 18

Arithmetic Series

The sum of the first n terms of an arithmetic series is given by the formula: Example 1. Find the sum of the first 20 terms of the arithmetic sequence 3, 13, 23, …..

. Example 2 Find the sum of the first 30 terms of an arithmetic sequence with first term 64 and common difference -3.

Example

Your turn! Find the sum of the first 25 terms of an arithmetic series 100 + 95 + 90 + 85 + … or sum(seq(105-5n,n,1,25)

Example 3. A new business is selling computers Example 3. A new business is selling computers. They predict to sell 20 computers in their first month, 23 in the 2nd, 26 in the 3rd and so on. How many months will pass before the company expects to sell their thousandth computer? We know that nSolve gives n=20.3794… so in their 21st month the sales will reach 1000 computers.

Using GDC with sum(seq Example 4 Find the sum of the first 6 terms of an arithmetic sequence with first term 2 and common difference 5.

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Write the first three terms and the last two terms of the following arithmetic series. What is the sum of this series?

What is the SUM of these terms? Written 1st to last. Written last to 1st. Add Down 50 Terms 71 + (-27) Each sum is the same.

Vocabulary of Arithmetic Sequence and Series It is important to note in an exam question whether it asks for the nth term or for the sum of the first n terms!

Your Turn

Ex 8.1.1 Qns 1 to 11 Ex 8.1.2 Qns 1-7 Ex 8.1.3 Qns 2, 4, 7, 9, 11