Cogito
Algebra 2 · Chapter 7 · Lesson 2
Series and Sigma Notation
Adding a list without writing it out.
12 problems · about 22 minutes · A-SSE.B.4, F-BF.A.2
What this lesson teaches
The student evaluates arithmetic and geometric series and reads sigma notation.
- A sequence is a list; a series is its total.
- Arithmetic sums use n(a₁ + aₙ) ÷ 2, the count times the average of the ends.
- Geometric sums use a₁(1 − rⁿ) ÷ (1 − r).
Warm Up
Straightforward practice. Get the method working first.
5 problemsWhat is the sum of 1 + 2 + ... + 50?
Answer 1275
Why 1275.
What is the difference between a sequence and a series?
Answer A series is the sum of the terms of a sequence.
Why A series adds up a sequence.
Sum of 1 + 2 + ... + 10?
Answer 55
Why 10(1 + 10) ÷ 2.
Sum of 2 + 4 + 6 + 8 + 10?
Answer 30
Why 5(2 + 10) ÷ 2.
A sum runs from k = 1 to k = 15. How many terms?
Answer 15
Why Count inclusively.
Build It Up
The same ideas with more to keep track of.
3 problemsA sum runs from k = 0 to k = 15. How many terms?
Answer 16
Why Zero counts too.
Geometric series 2 + 4 + 8 + 16. What is the sum?
Answer 30
Why Add them, or use 2(1 − 16) ÷ (1 − 2).
Geometric series 3 + 6 + 12 + 24 + 48. What is the sum?
Answer 93
Why 3(1 − 32) ÷ (1 − 2).
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each item as a sequence or a series.
Answer Sequence: 3, 7, 11, 15, The 20th term of a list · Series: 3 + 7 + 11 + 15, The total of the first 20 terms
Why A series is a list added up.
Sum of 5 + 10 + 15 + ... + 50?
Answer 275
Why 10 terms, so 10(5 + 50) ÷ 2.
The Sum: What is the sum of 1 + 2 + 3 + ... + 20?
Answer 210
Why 210.
The Seats: A theatre has 12 seats in row 1, 15 in row 2, 18 in row 3, and 10 rows in total. How many seats are there?
Answer 255 seats
Why 255 seats.