Hart Interactive ‐ ‐ Algebra 1 Lesson 4
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ALGEBRA I Exit Ticket Sample Solutions 1.
Write the first three terms in the following geometric sequences. Then write the explicit formula. for a.
, , and for b.
, , or , , . and 2.
Write an explicit formula for the geometric sequence. , , , ,… pattern , where starts at Homework Problem Set Sample Solutions S.37 1. Consider a sequence that follows a times pattern: , ,
a.
Write a formula for the starts with. th
,
, …. term of the sequence. Be sure to specify what value of your formula starting with b.
Using the formula, find the th
term of the sequence. c.
Graph the terms of the sequence as ordered pairs a coordinate plane. ,
on Lesson 4: Unit 7: Geometric Sequences
Sequences This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka‐math.org This file derived from ALG I‐M3‐TE‐1.3.0‐08.2015 68
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Hart Interactive ‐ ‐ Algebra 1 Lesson 4
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ALGEBRA I S.38 2. A radioactive substance decreases in the amount of grams by one‐third each year. If the starting amount of the substance in a rock is 1,452g, write a recursive formula and an explicit formula for a sequence that models the amount of the substance left after the end of each year. 1
f(n + 1) = f(n)  3
1
f(n) = 1452  3
(n – 1)
, n > 1, f(1) = 1452
(n – 1)
3. Write the first five terms of each geometric sequence. 1
2
B. f (1)  4 , r = 3 5 5
20,10,5, , 2 4
4, 12, 36, 108, 324 A. f (1)  20 , r = Use the formula for the general term (nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, f (1) , and common ratio, r. 5. Find f (12) when f (1)  5 , r = –2. 6. Find f (22) when f (1)  1000 , r =  1 . 7. Find f (15) when f (1)  9000 , r =  1 4. Find f (8) when f (1)  6 , r = 2. f(8) = 768 f(12) = –10,240 2
f (22)  
125
262144
3
f (15) 
1000
531441
Lesson 4: Unit 7: Geometric Sequences
Sequences This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka‐math.org This file derived from ALG I‐M3‐TE‐1.3.0‐08.2015 69
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Hart Interactive ‐ ‐ Algebra 1 Lesson 4
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ALGEBRA I S.39 Write a formula for the nth term of each geometric sequence. Then use the formula to find f (7) . 8. 3, 12, 48, 192, …… 9. 18,6,2, 2 ,..... 3
f (n )  3(4)
 1
f (n )  18  
3
f (7)  12,288 f (7) 
n 1
n 1
2
81
Find the first 5 terms of the following function. 10. f  n   f  n  1  2; f 1  3; n  2 11. f  n  
‐3, 5, ‐ 3, 5, ‐3 f  n  1
3
4
3
 1; f 1  3; n  2 3, 0, 1,  , 
13
9
Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for f(n) to find f(9). 12. 5, 1, 1 ,  1 ,.... 5
25
 1
f (n )  5   
 5
f (9) 
13. 0.07,0.007,0.0007,0.00007,... f (n )  0.07  0.1
f (9)  0.0000000007 n 1
1
78,125
n 1
S.40 14. A mine worker discovers an ore sample containing 500 mg of radioactive material. It is discovered that the radioactive material has a half life of 1 day. (This means that each day, half of the material decays, and only half is left.) Find the amount of radioactive material in the sample at the beginning of the 7th day. f(7) = 7.8125 mg Lesson 4: Unit 7: Geometric Sequences
Sequences This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka‐math.org This file derived from ALG I‐M3‐TE‐1.3.0‐08.2015 70
This work is licensed under a Creative Commons Attribution‐NonCommercial‐ShareAlike 3.0 Unported License.
Hart Interactive ‐ ‐ Algebra 1 Lesson 4
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ALGEBRA I 15. A culture of bacteria doubles every 2 hours. If there are 500 bacteria at the beginning, how many bacteria will there be after 24 hours? f(13) = 2,048,000 bacteria 16. You complain that the hot tub in your hotel suite is not hot enough. The hotel tells you that they will increase the temperature by 10% each hour. If the current temperature of the hot tub is 75º F, what will be the temperature of the hot tub after 3 hours, to the nearest tenth of a degree? f (4)  99.8o F S.41 CHALLENGE PROBLEMS 17.
Find the common ratio and an explicit form in each of the following geometric sequences. ,
a.
,
,
, ... , where ,
b.
,
,
, ... , where , , , , ... c.
, where d.
, ,
, , ... , where
18.
The first term in a geometric sequence is , and the th
term is . Find an explicit form for the geometric sequence. or
Lesson 4: Unit 7: Geometric Sequences
Sequences This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka‐math.org This file derived from ALG I‐M3‐TE‐1.3.0‐08.2015 71
This work is licensed under a Creative Commons Attribution‐NonCommercial‐ShareAlike 3.0 Unported License.
Hart Interactive ‐ ‐ Algebra 1 Lesson 4
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ALGEBRA I 19.
If , , , forms a geometric sequence, find the values of and . , so and 20.
Find the explicit form of a geometric sequence if and . or
, where or , where Lesson 4: Unit 7: Geometric Sequences
Sequences This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka‐math.org This file derived from ALG I‐M3‐TE‐1.3.0‐08.2015 72
This work is licensed under a Creative Commons Attribution‐NonCommercial‐ShareAlike 3.0 Unported License.