Lesson 4. Exit Ticket Sample Solutions. explicit formula. b. for and
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1 Exit icket Sample Solutions. Write the first three terms in the following geometric sequences. hen write the explicit formula. a. for and,, b. for and,, or,,.. Write an explicit formula for the geometric sequence.,,,, pattern, where starts at Homework Problem Set Sample Solutions S.7. Consider a sequence that follows a times pattern:,,,,. a. Write a formula for the th term of the sequence. Be sure to specify what value of your formula starts with. starting with b. Using the formula, find the th term of the sequence. c. Graph the terms of the sequence as ordered pairs, on a coordinate plane. : Geometric Sequences Unit 7: Sequences 68
2 S.8. 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,45 g, 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. f(n + ) = f(n) f(n) = 45 (n ), n >, f() = 45 (n ). Write the first five terms of each geometric sequence. A. f () 0, r = B. f () 4, r = 5 5 0,0,5,, 4 4,, 6, 08, 4 Use the formula for the general term (n th term) of a geometric sequence to find the indicated term of each sequence with the given first term, f (), and common ratio, r. 4. Find f (8) when f () 6, r =. 5. Find f () when f () 5, r =. f(8) = 768 f() = 0,40 6. Find f () when f () 000, r =. 7. Find f (5) when f () 9000, r = f () 5 f (5) : Geometric Sequences Unit 7: Sequences 69
3 S.9 Write a formula for the n th term of each geometric sequence. hen use the formula to find f (7). 8.,, 48, 9, 9. 8,6,,,... fn ( ) (4) n f (7),88 n f( n) 8 f (7) 8 Find the first 5 terms of the following function. 0. f nf n; f ; n. f n f n ; f ; n 4, 5,, 5,, 0,,, 9 Write a formula for the general term (the n th term) of each geometric sequence. hen use the formula for f(n) to find f(9).. 5,,,, ,0.007,0.0007, , f( n) 5 5 n f( n) n f (9) f (9) ,5 S 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 day. (his 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 7 th day. f(7) = 7.85 mg : Geometric Sequences Unit 7: Sequences 70
4 5. A culture of bacteria doubles every hours. If there are 500 bacteria at the beginning, how many bacteria will there be after 4 hours? f() =,048,000 bacteria 6. You complain that the hot tub in your hotel suite is not hot enough. he hotel tells you that they will increase the temperature by 0% each hour. If the current temperature of the hot tub is 75º F, what will be the temperature of the hot tub after hours, to the nearest tenth of a degree? S.4 f (4) 99.8 o F CHALLENGE PROBLEMS 7. Find the common ratio and an explicit form in each of the following geometric sequences. a.,,,,..., where b.,,,,..., where c.,,,,..., where d.,,,,..., where 8. he first term in a geometric sequence is, and the th term is. Find an explicit form for the geometric sequence. or : Geometric Sequences Unit 7: Sequences 7
5 9. If,,, forms a geometric sequence, find the values of and., so and 0. Find the explicit form of a geometric sequence if and. or, where or, where : Geometric Sequences Unit 7: Sequences 7
A sequence is an ordered list of numbers. Each number in a sequence is called a term. a 1, a 2, a 3,..., a n
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