Write a recursive rule for the geometric sequence shown on the graph. 7. 200 fn), 8. 10 (1, 10) 160 •(5, 162) 8. 120 80 4 (2, 3) (4, 54) 40 t1, 2) (3. 18) 2 (3, 0.9) (4, 0.27) 2.6) (5, 0.081) n 6. 8.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 16T
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I need help solving #7 &8 please and thanks!
Check Understanding
M Model wis
19.
number of sea to
Determine whether each sequence is geometric. If it is geometric, find the common ratio r.
from now. Supp
pear is three tim
1. 3,9, 27, 81, ..
2. 8, 4, 2, 1, ..
3. 6, 9, 12, 15, ...
previous year.
A. Write a recu
B. How many
Write a recursive rule for each geometric sequence. Then find the next three terms.
10, 20, 40, 80...
6. 5000, 1000, 200, 40, 8, ...
4.
5. 1, 5, 25, 125, ...
Write a recursive rule for the geometric sequence shown on the graph.
Write a recursive re
7.
Af(n)
200
8.
4fln)
10 (1, 10)
20. 4, 20, 100, 500.
• (5, 162)
22. 200, --80, 32,
160
8.
120
Fiad the indicated
6
23. 1, 8. 64, ...; St
80
4
26. Part of a geom
sequence. Thes
• (2, 3)
.(4, 54)
(3, 18)
40
(1, 2)
(3, 0.9)
(4, 0.27)
(5, 0.081) n
(2, 6)
Position nu
4.
6
8.
2
The heights to which a ball bounces after it is dropped are as follows: 72 inches on
the 1st bounce, 36 inches on the 2nd bounce, and 18 inches on the 3rd bounce. Let
f(n) = the height of the ball in inches on the nth bounce. The sequence defined by
f(n) is geometric.
9.
Term of the
27. (MP Reason
What is the 4
A. Graph the sequence.
Write a recursive
B. Write a recursive rule for the sequence.
C. What is the height of the ball on the 6th bounce to the nearest tenth of an inch?
28.
ffin)
1500
On Your Own
1200
Determine whether each sequence is arithmetic or geometric.
900
10. 200, 195, 190, 185, ...
11. 2, 6, 18, 54,..
12. 9, -3, 1,.
600
Find the common ratio r for each geometric sequence, Then use r to find the next
300
(2, 2
1, 5)
three terms.
13. 5, 15, 45, 135, ...
14. 243, 162, 108, 72, ...
15. -2, 6, -18, 54, ...
0.
Graph the seque
Attend to Precision The hours Myrón practices piano each week after he
starts taking lessons are given by the sequence 2, 3, 4.5, 6.75, ..
A. Is this a geometric sequence? Explain.
16.
30.
B. What is the next term in the sequence?
f(n)
17. (MP Reason Suppose you are given a geometric sequence where all the terms
are positive and 0 <r<1. Will the sequence be increasing or decreasing? Explain.
31. f(1) 200,
32.
Reason Suppose you are given a geometric sequence with r< 0. What will
be true about the signs of the ternis of the sequence? Explain.
Atter
in the first
Iwice the m
the numbe
18.
366
Nodule 14 Le
Transcribed Image Text:Check Understanding M Model wis 19. number of sea to Determine whether each sequence is geometric. If it is geometric, find the common ratio r. from now. Supp pear is three tim 1. 3,9, 27, 81, .. 2. 8, 4, 2, 1, .. 3. 6, 9, 12, 15, ... previous year. A. Write a recu B. How many Write a recursive rule for each geometric sequence. Then find the next three terms. 10, 20, 40, 80... 6. 5000, 1000, 200, 40, 8, ... 4. 5. 1, 5, 25, 125, ... Write a recursive rule for the geometric sequence shown on the graph. Write a recursive re 7. Af(n) 200 8. 4fln) 10 (1, 10) 20. 4, 20, 100, 500. • (5, 162) 22. 200, --80, 32, 160 8. 120 Fiad the indicated 6 23. 1, 8. 64, ...; St 80 4 26. Part of a geom sequence. Thes • (2, 3) .(4, 54) (3, 18) 40 (1, 2) (3, 0.9) (4, 0.27) (5, 0.081) n (2, 6) Position nu 4. 6 8. 2 The heights to which a ball bounces after it is dropped are as follows: 72 inches on the 1st bounce, 36 inches on the 2nd bounce, and 18 inches on the 3rd bounce. Let f(n) = the height of the ball in inches on the nth bounce. The sequence defined by f(n) is geometric. 9. Term of the 27. (MP Reason What is the 4 A. Graph the sequence. Write a recursive B. Write a recursive rule for the sequence. C. What is the height of the ball on the 6th bounce to the nearest tenth of an inch? 28. ffin) 1500 On Your Own 1200 Determine whether each sequence is arithmetic or geometric. 900 10. 200, 195, 190, 185, ... 11. 2, 6, 18, 54,.. 12. 9, -3, 1,. 600 Find the common ratio r for each geometric sequence, Then use r to find the next 300 (2, 2 1, 5) three terms. 13. 5, 15, 45, 135, ... 14. 243, 162, 108, 72, ... 15. -2, 6, -18, 54, ... 0. Graph the seque Attend to Precision The hours Myrón practices piano each week after he starts taking lessons are given by the sequence 2, 3, 4.5, 6.75, .. A. Is this a geometric sequence? Explain. 16. 30. B. What is the next term in the sequence? f(n) 17. (MP Reason Suppose you are given a geometric sequence where all the terms are positive and 0 <r<1. Will the sequence be increasing or decreasing? Explain. 31. f(1) 200, 32. Reason Suppose you are given a geometric sequence with r< 0. What will be true about the signs of the ternis of the sequence? Explain. Atter in the first Iwice the m the numbe 18. 366 Nodule 14 Le
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