Page 46 - Math Course 1 (Book 1)

Algebraic Equations

Find a Term in an Arithmetic REAL WORLD EXAMPLE
Sequence
TELEPHONE

Example CHARGES

For a telephone call to
India, a telephone company
Find the 11th term of 6, 9, 12, 15, … charges $8 for the f rst
minute and $4 for each
+1 +1 +1 additional minute.

How much does it cost for a 10-minute call?
Term Number 1 2 3 4 Make a table to organize the sequence and
(n)
f nd a rule.

Term (t) 6 9 12 15 Number of
Minutes (n) 1 2 3

+3 +3 +3 Cost (c) 8 12 16

The difference of the term numbers is 1.
The terms have a common difference of 3. The difference of the term numbers is 1.
The terms have a common difference of 4.
The common difference is 3 times the difference
of the term numbers. The pattern in the table shows the equation
c = 4m + 4.
This suggests that t + 3n. However, you need to If c = 4m + 4 or c = 4(10) + 4, then c = 44.
add 3 to get the exact value of t. Thus, t = 3n + 3.

Answer A 10-minute call would cost $44.
If n = 2, then t = 3(2) + 3 or 9.
Check
If n = 4, then t = 3(4) + 3 or 15.

To f nd the 11th term in the sequence, let n = 11
and solve for t. Your Turn!
t = 3n + 3 Write the equation.

= 3(11) + 3 or 36 Describe an Arithmetic Sequence
Describe the sequence 7, 14, 21, 28, … using words
and symbols.
Answer The 11th term is 36.
A. difference of term numbers: 7; common
difference: 1; equation: t = n + 3

B. difference of term numbers: 7; common
difference: 1; equation: t = 7n

C. difference of term numbers: 1; common
difference: 7; equation: t = n + 3

D. difference of term numbers: 1; common
difference: 7; equation: t = 7n

38