Arithmetic Series
9-4
Arithmetic Series
Today’s Objective:
I can find the sum of an arithmetic series.
The first four rows of chairs are set up
for a meeting. The seating pattern is to
continue through 20 rows. How many
chairs will there be in all 20 rows?
Series:
Sum of the terms of a sequence
Finite Series:
Has first and last term
6 + 9 + 12 + 15 + 18
Infinite Series:
Continues without end
3 + 7 + 11 + 15 + . . .
4 + 5 + 6 + 7 + . . . + 23
= 270
2 + 4 + 6 + ··· + 100
= 270
7 + 11 + 15 + ··· + 207
– 5 + 2 + 9 + 16 +··· + 268
Arithmetic Series
Explicit Formula = Linear
Slope = Common Difference
Find 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 in
their first week, and then improve their sales numbers
by two each week thereafter. One salesperson
qualified for the bonus with the minimum possible
number of sales.
How many sales did the salesperson make in week 50?
p. 591: 9-45 mult. of 3
and 47
How many sales did the salesperson make in all 50 weeks?
Calculator Notes:
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explicit formula, x, lower limit, upper limit
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The concepts of arithmetic series, including finding the sum of a series, finite series, infinite series, summation notation, explicit formulas, and practical applications such as bonus calculations. Learn about seating arrangements, sales numbers, and more.
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Presentation Transcript
9-4 Arithmetic Series Today s Objective: I can find the sum of an arithmetic series.
The first four rows of chairs are set up for a meeting. The seating pattern is to continue through 20 rows. How many chairs will there be in all 20 rows? 4 + 5 + 6 + 7 + . . . + 23 = 270 20 4 2 + 4 + 6 + + 100 50 = 270 2( + ) ?20= 23 Series: Sum of the terms of a sequence Finite Series: Has first and last term 6 + 9 + 12 + 15 + 18 2( + ) ?50= 100 2 Infinite Series: Continues without end 3 + 7 + 11 + 15 + . . . = 2550 Sum of a Finite Arithmetic Series ?1+ ?2+ ?3+ + ?? ??=? 2(?1+ ??)
Summation Notation ????? ???? ?????? 5 + 2 + 9 + 16 + + 268 40 ???????? ??????? 7? 12 ?????? ???? ?????? 7 + 11 + 15 + + 207 51 4? + 3 ?=1 Arithmetic Series Explicit Formula = Linear Slope = Common Difference ? = 1 ???????? ??????? ????? ???? ?????? ??= 7 + (? 1) 4 = 7 + 4? 4 207 = 4? + 3 204 = 4? 51 = ? = 4? + 3
Find the sum of a Finite Arithmetic Series 40 4 13 = 1 ?1= ?3 (3? 8) 23 33 = 8 = 27 ?2= ?3= ?=1 ?=1 ??=? 2(?1+ ??) 43 = 64 ?4= 100 ?1= 3 1 8 = 5 ?40= 3 40 8 = 112 40 2( 5 + 112)= 2140 ?40=
A company pays a $10,000 bonus to salespeople at the end of their first 50 weeks if they make 10 sales in their first week, and then improve their sales numbers by two each week thereafter. One salesperson qualified for the bonus with the minimum possible number of sales. How many sales did the salesperson make in week 50? ?50= 10 + (50 1) 2 How many sales did the salesperson make in all 50 weeks? = 108 p. 591: 9-45 mult. of 3 and 47 50 2(10 + 108) = 2950 ?50=
