Page 41 - Math Course 1 (Book 1)

Arithmetic Sequences

MO. 1 - L7b

Write Formulas for B. Find the 12th term in the sequence.
Arithmetic Sequences Replace n with 12 in the equation written in part A.

n
Let’s Begin a = 9n - 8 Equation for the nth term.

a = 9(12) - 8 Replace n with 12.
12

Examples a = 100 Simplify.
12

REAL WORLD EXAMPLE

Answer 100
MONEY
The arithmetic sequence
1, 10, 19, 28, … represents the
total number of dollars Erin
has in her account after her C. Graph the f rst f ve terms of the sequence.
weekly allowance is added.
n 9n - 8 a n (n, a )
n
In this sequence, the f rst term, a1, is 1.
Find the common difference.
1 9 (1) - 8 1 ( 1, 1 )
1, 10, 19, 28,
2 9 (2) - 8 10 ( 2, 10 )

+9 +9 +9 3 9 (3) - 8 19 ( 3, 19 )

The common difference is +9.
4 9 (4) - 8 28 ( 4, 28 )
5 9 (5) - 8 37 ( 5, 37 )
Use the formula for the nth term to write an
equation.
Answer
a = a1 + ( n - 1) d Formula for the a n
n
nth Term.
40
a = a1 + ( n - 1) 9 a1 = 1, d = 9 35
n
30
a = 1 + 9n - 9 Distribute property 25
n

20
a = 9n - 8 Simplify 15
n
10
For n = 1, 9(1) – 8 = 1.
Check For n = 2, 9(2) – 8 = 10. 5
For n = 3, 9(3) – 8 = 19, and so on.
0 1 2 3 4 5 6 n

n
Answer a = 9n - 8 The points fall on a line. The graph of an
arithmetic sequence is linear.

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