VOCABULARY: 4errrr- Gemmorrdifferenee first tcrm --recarsive-etp3aticm- -terrrrntiriciber: An organized list of numbers.

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1 ALGEBRA 1 Ch 5 Closure Sequences Name: Al--- VOCABULARY: -afithi netic 'sequence- ex-pernentiflittfon- 4errrr- Gemmorrdifferenee first tcrm --recarsive-etp3aticm- -terrrrntiriciber: contrrron-ratio- -geemetrie-sequence -seeittenee-- -4(69 S -sequence-generator- y-intercept.explicit-eettratiott --rineaftinetion An organized list of numbers. A Al?WV, il bc-r-eta-c A sequence generated by adding or subtracting a constant amount to the previous term to get the next term. A sequence generated by multiplying or dividing a constant amount to the previous term to get the next term. P D7 4. (i..-6m4 vim.6y1 691_, 5. This value tells you how to find the following term when you know the previous term. This is the sequence generator in an arithmetic sequence. _461.1& 4m.34), i 6. This is the sequence generator in a geometric sequence. it /kw Afi/221...t 7. a A_ ,./..Aii--AY1/1 41.,1-1A-1,, 9. lqte 0-1/1 ( /Y Lot-be Ai/4F I id-1/1/1 14. The common ratio in a geometric sequence is also called this. An arithmetic function is also this. A geometric function is also this. A single number within a sequence. This is indicated by the variable n. It represents where a number is located within a sequence. 4 (4) An equation for a sequence that allows you to determine the value of any term based on its term number. An equation for a sequence that has two parts. To use it, you need to know the previous term to calculate the next term. The first number in a sequence di tos 17. d.,0-1/17, Another name for the first term. The mathematical way of indicating the term before the first term. This is where a graph crosses the y-axis. In a sequence, this value helps us generate the explicit formula, but it does not exist on the graph. The set of all input values in a function. In a sequence, it's all Natural numbers.

2 CONCEPTS: 1. Each of the explicit functions listed defines a sequence. List the first four terms of each sequence and state whether each sequence is arithmetic, geometric or neither. a. t(n) = 5n + 2 b. an = 3-8n, /2- i S arithmetic) geometric neither afithmetic geometric neither C. t(n) = n - fl d. t(n) = (-2)" CR 1g /1? to /6, arithmetic geometric arithmetic ometri neither e. a,, in S _6 '1 ynri meti geometric neither f. an =100(+)" 25 2s i MD / O, arithmetic metric neither 2. Each of the explicit functions listed defines a sequence. List the first four terms of each sequence and state whether each sequence is arithmetic, geometric or neither. a. 41)=5 t(n +1) = t(n)+ 3 b. t(1) =100 t(n +1) = t(n)* 1.5 cz /1 / 4 too, / go 22-6 rithroreti geometric neither arithmetic neither t(1) = -3 41)=12 c. d. t(n +1), t(n) (-2) t(n +1) = t(n) el" G, 1 arithmeticgeometric neither ri hmetic geometric neither 41)=4 t(1)=1 e. f. t(n +1), t(n) +'± t(n +1) = (t(n)) " 2.-- if II I 11 it-3.s ' :is / /,ZS rithmeti geometric neither arithmetic geometric rraitei rd

3 3. For each of the following sequences, write an explicit equation, a recursive equation, then calculate the 25th term in the sequence. Show all work. a. 14, 10,6, 2,... b. -16,-13,-10, -7, 3 explicit: --L. (v ) +-(o = / _ e -E (25) -.2 e 4, c. 32, 64, 128, 256,.4( 2- explicit: 4-64) ,(v\A /A) 4-3 -Las) -H r- d. 5, -5, 5, -5, explicit: -E (vn ) (2 )n tie.) 'LL Y\ fa eb explicit: -LC4) = +(i) ----G +IA+ + (IA) -E(2s) = 17.0(7-i5 S-3(so r7oi )74 4. Create a graph for the following sequences. State whether the sequence is arithmetic or geometric. a. t(n)=-3n+ 15 b. t(n)= 2+1.5n rithmetic geometric neither rifhmetic geometric neither

4 c. t(n)=50(0.8)" d. t(n)=5(1.25f arithmetic neither arithmetic neither 52 " x Find the missing terms for this sequence: 11 15, 11,, 3, Write an explicit equation for this sequence: (tt) Pi 4-23 Is the number in this sequence? If so, what term is it? ( DI 4i` - 4 If not, explain why not. (40; --L C -get vt--- / Fo c lieicir re- 6. Find the missing terms for this sequence: ID, 20, 40, `EV, 160, Write an explicit equation for this sequence: re( ) - 5 (2-) Is the number 405 in this sequence? Vki0 If so, what term is it? 1?)".41,-eia (en_ e-r If not, explain why not. 1%11 &6) Find the missing terms for this sequence: 14 18, 21 ; 23, 2-4 1/4.--m < r-2p---" el) Is this sequence arithmetic, geometric, or neither? IA P...t:41".tit What is the 10th term in this sequence? I 2' ( A)

5 8. Peachy Orchard Developers are preparing land to create a large subdivision of single-family homes. They have already built 10 houses on the site. Peachy Orchard plans to build four new homes every month. a. Create a table of values that will show the number of houses in the Peachy Orchard subdivision over time. b. Graph the sequence. Watch the scale! helb14-4 Ct_ s c. Write an equation relating the number d. How long until all 250 lots are built? of houses built over time =.1- I 0 2 5{0 7-- n (co v14_61^9-1" (00 n 9. Rosa tripped and fell into a muddy puddle at lunch (she was so embarrassed!), she knew exactly what would happen: within one minute, the two girls who saw her fall would each tell one person what they had seen. Within the next minute, those four students would each tell one more person. Rosa knew this could continue until everyone in the whole school was talking about her muddy experience. If there are 2016 students in the school, how many minutes would it take for everyone to know? a. Create a table of values that will show the number of people in school who know over time. b. Graph the sequence. Watch the scale! I I I 4 5 fi 7 B x if.a41' c. Write an equation relating the number of people who know over time. d. How long until all 2016 students know?!" C 4- g,k(,) 1,J( 1 2,1 25(r 61a /ov-i,2041; -He\ ) 2(0`1` f ins-tnalet -foikt /edit '144A-01-19n4-4:6.-

I. Recursive Descriptions A phrase like to get the next term you add 2, which tells how to obtain

I. Recursive Descriptions A phrase like to get the next term you add 2, which tells how to obtain Mathematics 45 Describing Patterns in s Mathematics has been characterized as the science of patterns. From an early age students see patterns in mathematics, including counting by twos, threes, etc.,