Practice Questions Ex 3.4: 1, 3, 5, p99

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Presentation transcript:

Practice Questions Ex 3.4: 1, 3, 5, p99 2. Series Practice Questions Ex 3.4: 1, 3, 5, p99

Series Definitions Sigma Notation: A series adds the terms in a sequence: Sigma Notation:

Arithmetic Series Examples Find each sum: Find the sum of the first 20 terms of the series – 2 + 1 + 4 + 7 + 10 + ...... 3. Find the sum of the first 35 terms of the series

Arithmetic Series Examples An arithmetic series has a third term of 0. The sum of the first 15 terms is −300. What is the first term and the sum of the first ten terms? 5. A new business is selling home computers. They predict that they will sell 20 computers in their first month, 23 in the second month, 26 in the third and so on, in arithmetic sequence. How many months will pass before the company expects to sell their thousandth computer?

Geometric Series Examples 6. Find each sum: 7. Sum this series to 7 terms: 8. Sum this series to 12 terms:

Geometric Sequences Examples 9. The 2nd term of a geometric series is −30 and the sum of the first two terms is −15. Find the first term and the common ratio.

Combination Example A geometric sequence has the same first term as an arithmetic sequence. The 3rd term of the geometric sequence is 48, which is the same as the 10th term of the arithmetic sequence. The 10th term of the arithmetic sequence is four times the 2nd term of the geometric sequence. Find the common difference of the arithmetic sequence and the common ratio of the geometric sequence.

Combination Example Bo-Youn and Ken are beginning savings accounts. Bo-Youn adds $1 the first week, $2 the 2nd week, $4 in the 3rd week and so on, in geometric progression. Ken adds $10 the 1st week, $20 the 2nd week, $30 the 3rd week and so on, in arithmetic progression. After how many weeks will Bo-Youn have saved more than Ken?