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Sums of Sums and Series

Sums of Sums and Series. When you know two terms and the number of terms in a finite arithmetic sequence you can find the sum of the terms.

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Sums of Sums and Series

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  1. Sums of Sums and Series

  2. When you know two terms and the number of terms in a finite arithmetic sequence you can find the sum of the terms. A series is the indicated sum of the terms of a sequence. A finite series, like a finite sequence, has a first term and a last term, while an infinite series continues without end. What is the difference between a sequence and a series? Look above and make your own conclusion. Which of the above sequences or series does this formula work with?

  3. n is the number of terms Sn means sum of the series Finding the Sum of a Finite Arithmetic Series What is the sum of the even integers from 2 to 100? The series 2 + 4 + 6 + . . . + 100 Is arithmetic with first term 2, last term 100 and common difference 2. The sum is What is the sum of the finite arithmetic series? But how do we figure out how many terms there are??

  4. Using the Sum of a Finite Arithmetic Series A company pays a $10,000 bonus to salespeople at the end of their first 50 weeks if they make 10 sales their first week, and then improve their sales numbers by two each week thereafter. One sales person qualified for the bonus with the minimum possible number of sales. How many sales did the salesperson make in week 50? How many in all 50 weeks? Week one = 10 sales They add two sales per week for 50 weeks so, and The salesperson made 108 sales in week 50 The salesperson made 2950 sales over 50 weeks

  5. The company in the last problem also has an alternative bonus plan. It pays a $5000 bonus if a new salesperson makes 10 sales in the first week and then improves by one sale per week thereafter. One salesperson qualified for this bonus with the minimum number of sales. How many sales did the salesperson make in week 50? a1 = 10 d =1 How many sales in all 50 weeks? in 50 weeks

  6. You can use the Greek capital letter sigma, , to indicate a sum. With it you use limits to indicate how many terms you are adding. Limits are the least and greatest values of n in the series. You write the limits below and above theto indicate the first and last terms of the series. For example, you can write the series To find the number of terms in a series written in summation form, subtract the lower limit from the upper limit and add 1. The number of terms in the series above is The series has 106 terms. Find the number of terms in the summation The series has 94 terms.

  7. Writing a Series in Summation Notation What is the summation notation for the series? The sequence 7, 11, 15, . . . , 203, 207 is arithmetic with a first term of and common difference Use the explicit formula for arithmetic sequences The answer is A. Since we know the first summation equation is correct

  8. What is the summation notation for the series? a. -19 + -14 + -9 + . . . + 221 + 226 b. 20 + 18 + 16 + . . . + -24 + - 26

  9. We can use the calculator to solve the summations. Use 2nd 0 (T) up arrow enter to get sum( Then 2nd 0 (S) down 9 times enter to get seq( Type in equation, <variable to solve for>, <upper bound>, <lower bound>) This works for a TI-83, other calculators may have different steps. Newer TI calculators may look exactly as the summation notation is shown.

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