hvvrq $ulwkphwlf 6htxhqfhv dqg 6hulhv - NCPN
hvvrq $ulwkphwlf 6htxhqfhv dqg 6hulhv - NCPN
hvvrq $ulwkphwlf 6htxhqfhv dqg 6hulhv - NCPN
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
INSTRUCTION<br />
Tell students that the arithmetic<br />
mean of two numbers is the<br />
number that is equally distant<br />
between the two numbers in<br />
addition.<br />
Point out that since there is a<br />
common difference between<br />
consecutive terms in an arithmetic<br />
sequence, that the difference<br />
between every other term is also a<br />
constant. The difference between<br />
every other term is twice the<br />
common difference.<br />
Answer to Critical<br />
Thinking<br />
Answers will vary. Sample answer:<br />
Let d represent the common<br />
difference of the sequence. Then<br />
the first missing term is 11 + d,<br />
and the second missing term is<br />
11 + d + d, or 11 + 2d, and<br />
the next term, 32, is equal to<br />
11 + 2d + d, or 11 + 3d. Solve<br />
the equation 11 + 3d = 32 for d<br />
to find the missing terms: 18 and<br />
25.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
105 135 <br />
2<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
Enriching the Lesson<br />
Show students the following alternative way to determine<br />
the missing term in Example 2.<br />
Step 1: The difference between the terms 105 and 135 is 30.<br />
Step 2: Because the difference between every other term in an arithmetic<br />
sequence is twice the common difference, the common difference is<br />
30÷2 = 15.<br />
Step 3: Adding the common difference to 105 yields a missing term of 120.<br />
398 Chapter 9 Sequences and Series
Change language