NJCTL



Arithmetic Sequences – Class WorkFind the common difference in the sequence and then write the next 3 terms in the sequence.d=729, 36, 43d=419, 23, 27d=-1220, 8, -4d=-3-7, -10, -133, 7,11, 15, …2. 1, 8, 15, 22, …3. 5, 2, -1, -4, …d=1.36.5, 7.8, 9.168, 56, 44, 32, …5. 1.3, 2.6, 3.9, 5.2, …Use the given information to write the first 5 terms of the sequence and the 20th term.3, 9, 15, 21, 27a20=11710, 4, -2, -8, -14a20=-1044, 12, 20, 28, 36a20=156a1= 4, d= 87. a1= 10, d= -68. a2= 9, d= 6-38, -33, -28,- 23, -18a20=574, 7, 10, 13, 16a20=61a15= 32, d= 510. 4, 7, 10, 13, …Solve the following questions.d=3.2What is the common difference when a1=8 and a11=40?n=12a20=-83What is 20th term if a1=12 and a10= -33?13. If a1=12, an=111 ,and d = 9, what is n?$7000; 10 carsTom works at a car dealership selling cars. If he makes $4000 a month and $250 per car he sells, how much did he make in July if he sold 12 cars? In August he made $6500, how many cars did he sell?Find the missing term(s) in the sequence.9, 1463, _ , 916. 4, _ , _ , 191, -332, 44, 565, _ , _ , -718. 20, _ , _ , _, 68 Arithmetic Sequences – HomeworkFind the common difference in the sequence and then write the next 3 terms in the sequence.d=-30, -3,-6d=1127, 38, 49d=938, 47, 562, 11, 20, 29, …20. -17, -6, 5,16, …21. 12, 9, 6, 3, …d=1.49.9, 11.3, 12.7d=-14-11, -25, -3945, 31, 17, 3, …23. 4.3, 5.7, 7.1, 8.5, …Use the given information to write the first 5 terms of the sequence and the 20th term.-5, 9, 23, 37, 51a20=26110, 2, -6, -14, -22a20=-1424, 7, 10, 13, 16a20=61a1= 4, d= 325. a1= 10, d= -826. a2= 9, d= 14-66, -59, -52, -45, -38a20=67-1, 5, 11, 17, 23a20=113a15= 32, d= 728. -1, 5, 11, 17, …Solve the following questions.a20=-74d=4.1$8000; 24 carsn=8What is the common difference when a1=3 and a11=44?What is 20th term if a1=2 and a10= -34?31. If a1=22, an=78 ,and d = 8, what is n?Tom works at a car dealership selling cars. If he makes $4000 a month and $250 per car he sells, how much did he make in July if he sold 16 cars? In August he made $10,000, how many cars did he sell?Find the missing term(s) in the sequence.11, 19104, _ , 1634. 3, _ , _ , 275, -221, 30, 3912, _ , _ , -936. 12, _ , _ , _, 48 Arithmetic Series – Class WorkFind the indicated Sn.S10=485S12=258a1 = 5, a12 = 38, find S1238. a1 = 8, a10 = 89, find S10S8=256S9=-108a1 = 12, a9 = -36, find S940. 4, 12, 20, 28, … find S8Sn=663S12=-5412, 9, 6, 3, … find S1242. 15 + 18 + 21 + … + 63, find Sn S9=-18a1= 10 , d= -3 find S9Evaluate the following6060a=154a45. b=382b-1c=1215-2c47. d=8223d+1690-108Arithmetic Series – HomeworkFind the indicated Sn.S11=418S14=-154a1 = 2, a14 = -24, find S1449. a1 = 18, a11 = 58, find S11S13=546S8=-20a1 = 15, a8 = -20, find S851. 6, 12, 18, 24, … find S13Sn=535S11=-2218, 14, 10, 6, … find S1153. 22 + 29 + 36 + … + 85, find Sn S12=-12a1= 10 , d= -2 find S12Evaluate the following4875a=155a56. b=382b-3915-162c=1215-3c58. d=8224d+1Geometric Sequences – Class WorkFind the common ratio in the sequence and then write the next 3 terms in the sequence.r=-3324, -972, 2916r=280,160, 3205, 10, 20, 40, …60. 4, -12, 36, -108, …r=1.530.375,45.5625, 68.34375r=-12 1,-12,14 16, -8, 4, -2, …62. 6, 9, 13.5, 20.25, …Use the given information to write the first 4 terms of the sequence and the 10th term.12, 6, 3, 1.5a10=0.02343756, 18, 54, 162a10=118098a1=6 and r=364. a1=12 and r=.55, 10, 20, 40a10=25608, 32, 128, 512a10=2097152a1=8 and r= 466. a3=20 and r=2a12=20,480 cellsA cell reproduces by splitting in half every half hour. How many cells will there be in 6 hours if at the start there were 10?Find the missing term(s) in the sequence.15, 4524 or -244, _ , 14469. 5, _ , _, 1356, _ , _, -.7571. 7, _ , _ , _ , 437535, 175, 875or-35, 175, -875-3, 1.5Geometric Sequences – HomeworkFind the common ratio in the sequence and then write the next 3 terms in the sequence.r=-296, -192, 384r=4512,2048, 81922, 8, 32,128, …73. 6, -12, 24, -48, …r=-1.25-9.765625, 12.20703125, -15.25878906r=-12 1.25, -0.625, 0.312520, -10, 5, -2.5, …75. -4, 5, -6.25, 7.8125 , …Use the given information to write the first 4 terms of the sequence and the 10th term.20, 10, 5, 2.5a10=0.03906258, 80, 800, 8000a10=8000000000a1=8 and r=1077. a1=20 and r=.54, 12, 36, 108a10=7873216, -32, 64, -128a10=-8192a1=16 and r= -279. a3=36 and r=3a20=20,971,520 cellsA cell reproduces by splitting in half every 15 minutes. How many cells will there be in 5 hours if at the start there were 20?Find the missing term(s) in the sequence.30, 18012 or -124, _ , 3682. 5, _ , _, 108028, 112, 448or-28, 112, -44848, 3846, _ , _, 307284. 7, _ , _ , _ , 1792Geometric Series – Class WorkFind the indicated Sn.S12=-8190S8=22960a1=7, r=3, and n= 8, find S886. a1=6, r= -2, and n= 12, find S12S8=390624S6=15.75a1=8, r=.5, and n= 6 find S688. a1=4 and a8 = 312500, find S8S6=15624a1=4 and a8 = 312500, find S6Evaluate the following9380n=142?3n-191. n=153?2n-1n=16-2?(-2)n-193. n=156?(-.5)n-14.12542Geometric Series – HomeworkFind the indicated Sn.S7=32770S9=2929686a1=6, r=5, find S995. a1=10, r= -4, find S7S8=39360S8=95.625a1=48, r=.5, find S897. a1=12 and a8 = 26244, find S8S6=4368a1=12 and a8 = 26244, find S6Evaluate the following10920240n=146?3n-1100. n=168?(4)n-1-1020-321.71875n=17-10?(1.5)n-1102. n=1812?(-2)n-1Infinite Geometric Series – Class WorkFind the sum of the infinite series if one exists.-83 not possible15a1= 5 and r= 2/3104. a1= -4 and r=-1/2105. a1= 6 and r=5/412872-1285=-25.6 a2=8 and r=-1/4107. 32 + 24 + 18 + 13.5+…108. 12 + 10 + 253 + 12518 + …x=1∞313n-1110. x=1∞-254n-1111. x=1∞6-19n-1274=5.4 not possible92=4.5 Infinite Geometric Series – HomeworkFind the sum of the infinite series if one exists.494=12.25 not possible6a1= 3 and r= 1/2113. a1= -6 and r=-3/2114. a1= 7 and r=3/7not possible160-252=-12.5 a2=12 and r=-3/5116. 40 + 30 + 22.5 + 16.875+…117. 5 – 6 + 365 – 21625 + …x=1∞4-13n-1119. x=1∞-856n-1120. x=1∞12-12n-18-483Special Sequences – Class WorkIdentify the sequence as arithmetic, geometric, or neither. Write the first 5 terms.Arithmetic-4, 4, 12, 20, 28Geometric6, -18, 54, -162, 486Neither3, 14, 58, 234, 938a1=3; an= 4an-1 + 2122. a1=6; an= -3an-1 123. a1=-4; an= an-1 + 8Geometric1, 6, 36, 216, 1296Arithmetic8, 10, 12, 14, 16Neither-7, -15, -31, -63, -127a1=-7; an= 2an-1 -1125. a1=8; an= an-1 + 2126. a1=1; an= 6an-1 Neither10, 8, 12, 4, 20Neither-9, 6, 6, 36, 156a1=-9;a2=6; an= 4an-1 + 2an-2128. a1=10; a2= 8; an= -1an-1 + 2an-2Special Sequences – HomeworkIdentify the sequence as arithmetic, geometric, or neither. Write the first 5 terms.Arithmetic-14, -19, -24, -29, -34Geometric8, -16, 32, -64, 128Arithmetic2, 10, 18, 26, 34a1=2; an= an-1 + 8130. a1=8; an= -2an-1 131. a1=-14; an= an-1 – 5Neither5, 27, 137, 687, 3437Geometric12, 36, 108, 324, 972Geometric-1, -6, -36, -216, -1296a1=-1; an= 6an-1 133. a1=12; an= 3an-1 134. a1=5; an=2 + 5an-1 Neither1, 1, 2, 3, 5Neither-4, 3, -6, -3, -24a1=-4;a2=3; an= 2an-1 + 3an-2136. a1=1; a2= 1; an= an-1 + an-2Binomial Theorem – Class WorkConsider the binomial expansion of 4x-2yn to identify the term.-1280x2y3-96x2y2nd term when n=3138. 4th term when n =548xy228672x2y67th term when n=8140. 3rd term when n=3-1032192x4y56th term when n=9Binomial Theorem – HomeworkConsider the binomial expansion of 2a-4bn to identify the term.-10240a3b3-128a3b2nd term when n=4143. 4th term when n =616b257344ab67th term when n=7145. 3rd term when n=2-8257536a5b56th term when n=10Sequences and Series Unit ReviewMultiple ChoiceThe sequence 2, 6, 10, 14,… hasDa common ratio of 3a common difference of 3a common ratio of 4a common difference of 4The sequence 8, -4, 2, -1 ,… hasCa common ratio of 1/2a common difference of 1/2a common ratio of -1/2a common difference of -1/2The next term in the sequence 7, 13, 19, 25 is B6313248The next term in the sequence 64, 48, 36, 27 isB2020.2520.521What is the common difference in this arithmetic sequence: 4, __, __,__, 25A5.256.577.4What is the common ratio in this geometric sequence: 4, __, __, 108±3B3±2727What is the common ratio in this geometric sequence: 32, __, __, __, 2A±.5.5±22a1 = 6 and d = 8 find S6D4648108156a1=8 and r = -4, find S6C-10920-8192-6552-12n=483n=D24367290n=192n-5=A45402813n=1∞4-12n-1C02.52 2/3not possibleFind the first 5 terms of a1 = 3 and an= 2an-1D3, 6, 9, 12, 153, 5, 7, 9, 113, 6, 12, 24, 363, 6, 12, 24, 48Find the first 5 terms of a1 = 2 and a2=8 and an= an-1 + an-22, 8, 10, 18, 28A2, 8, 10, 12, 202, 8, 16, 32, 642, 8, 16, 24, 32The sequence 1, 1, 2, 3, 5, 8, … is CarithmeticgeometricFibonacciNone of the aboveThe coefficient of the 3rd term of (2x – 3y)4 is-216B216-9696Extended ResponseYour rich uncle wants to hire you to work for his company for 30 days. He offers to pay you (A) $1000 per day or (B) 1 cent the first day and double the pay each day thereafter.$30,000How much money do you make in 30 days of pay A?$5,368,709.12How much do you make on day 30 of pay B?$10,737,418.23How much money do you make in 30 days of pay B?Given the sequence 2, ___, ___, -16-4, 8What are the missing terms if the sequence were geometric?-4, -10What are the missing terms if the sequence were arithmetic?n=142(-2)n-1=-10 n=148-6n=-28 What is the sum of each sequence from part a and b. Use Sigma notation.Given the arithmetic sequence of 4, 10, 16, 22, …a20=118What is a20?an=-2+6nWhat is an?S20=1220What is S20?Sn=n2(2+6n) What is Sn?Given the geometric sequence of 20, -10, 5, -2.5, …a10=-5128=-0.0390625 What is a10?an=20(-12)n-1 What is an?S10=1705128=13.3203125 What is S10?Sn=403(1-(-12)n) What is Sn?S∞=403=13.3 What is S∞? ................
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