, n ≥ 3.
c. First, find the 13th and 14th terms by writing out 14 terms of the sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,
233, 377.
Then, a13 = 233 and a14 = 377. Thus, a15 = a13 + a14 or 610.
d. Sample answer: Fibonacci sequence is not an arithmetic sequence since there is no common difference.
31. ERROR ANALYSIS Patrick and Lynda are working on a math problem that involves the sequence 2, –2, 2, –2, 2,
… . Patrick thinks that the sequence can be written as a recursive formula. Lynda believes that the sequence can be
written as an explicit formula. Is either of them correct? Explain.
SOLUTION:
Both; sample answer: The sequence can be written as the recursive formula a1
= 2, an
= (–1)an – 1
, n ≥ 2. The
sequence can also be written as the explicit formula an
= 2(–1)n – 1
.
32. CHALLENGE Find a1
for the sequence in which a4
= 1104 and an
= 4an – 1
+ 16.
SOLUTION:
Find a3
first.
Find a2
next.
interest rate compounded monthly. How much money will
Nicholas have after 5 years?
SOLUTION:
After 5 years, Nicholas will have $2664.35.
47. TOURS The Snider family and the Rollins family are traveling together on a trip to visit a candy factory. The
number of people in each family and the total cost are shown in the table below. Find the adult and children’s
admission prices.
SOLUTION:
Let a be the admissions cost for adults and c the admission cost of children.
Then 2a + 3c = 58 and 2a + c = 38.
So, tickets for adults cost $14 and tickets for children cost $10.
Write each equation in standard form.
48.
SOLUTION:
49.
SOLUTION:
50.
SOLUTION:
51.
SOLUTION:
52.
SOLUTION:
53.
SOLUTION:
Simplify each expression. If not possible, write simplified.
54.
SOLUTION:
55.
SOLUTION:
56.
SOLUTION:
57.
SOLUTION:
There are no like terms, so the expression is simplified.
58.
SOLUTION:
59.
SOLUTION:
There are no like terms, so the expression is simplified.
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