Answer:
ito ay dapat sinasagutan niyo wag kayo tanong ng tanong
, 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.
Find a3
first.
Find a2
next.
interest rate compounded monthly. How much money will
Nicholas have after 5 years?
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.
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.
49.
50.
51.
52.
53.
Simplify each expression. If not possible, write simplified.
54.
55.
56.
57.
There are no like terms, so the expression is simplified.
58.
59.
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Answers & Comments
Answer:
ito ay dapat sinasagutan niyo wag kayo tanong ng tanong
, 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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