Download Discovery Lesson-12.1

Guided Discovery Lesson
Section 12.1-Arithmetic Sequences and Series
I. Arithmetic Sequences
A. Basic Ideas & Terms. Read page 656 through Example 1, page 657.
1. What is a sequence?
2. What are the terms of a sequence?
3. How is the first term of a sequence denoted? How is the nth term
denoted?
4. What is an arithmetic sequence?
5. Work problems 5, 7, 9, 11 & 13 on page 660.
B. Finding the nth term of an arithmetic sequence. Read p 657 through
Example 4 on page 658.
1. What is the formula for finding the nth term of an arithmetic sequence?
2. What does each of the four terms in this formula represent?
3. What are arithmetic means of nonconsecutive numbers of an arithmetic
sequence?
4. Work problems 15, 16 and 17 on page 660.
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II. Arithmetic Series. Read page 658-659.
A. What is the definition of an arithmetic series?
B. What is the formula for the sum of the first n terms of an arithmetic series?
C. In this formula, the sum can be thought of as being the product of a certain
number of terms and the average of two particular terms? Which two terms are
“averaged?” By how many terms should this average be multiplied?
D. Use this formula and the expression for the nth term to obtain a formula for
the sum in terms of n, d, and a1 .
E. Use either of these two formula to work problem18 on page 660 and to
compute the total number of nickels that would be collected in a 31-day month that was
descried at the beginning of the class.
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