Questions on Algebra: Sequences of numbers, series and how to sum them answered by real tutors!

Tutors Answer Your Questions about Sequences-and-series (FREE)

Question 1143265: Predict the general term, or nth term, an, of the sequence

-15,75,-375,1875,-9375,...
Click here to see answer by josgarithmetic(39618)

Question 1143289: On a particular day, the wind added 5 miles per hour to Jaime's rate when she was rowing with the wind and subtracted 5 miles per hour from her rate on her return trip. Jaime found that in the same amount of time she could row 42 miles with the wind, she could go only 22 miles against the wind.
What is her normal rowing speed with no wind?
Click here to see answer by Theo(13342)

Question 1143335: Looking for a missing number in the interior of a sequence and can't figure out how to get there.
1, 4, 27, X, 3761
Click here to see answer by Edwin McCravy(20056)

Question 1143375: a sub n = -37 n = 22 d = -3
Click here to see answer by greenestamps(13200)

Question 1143446: Harmonic sequence:
2,2/3,2/5,2/7 with solution
What is the next term in the harmonic sequence 1/11,1/15,1/19,1/23,...? With solution
What is the nth term of the harmonic sequence 1/2,1/4,1/6,1/8 with solution
Click here to see answer by Edwin McCravy(20056)

Question 1143488: if a, b, c are in hp show that 1/a + 1/b+c, 1/b + 1/(c+a), 1/c + 1/(a+b) are
also in hp.
Click here to see answer by Edwin McCravy(20056)

Question 1143485: If a, b, c are in hp, show that 1/a + 1/b+c, 1/b + 1/c+a, 1/c + 1/a+b are also in hp
Click here to see answer by ikleyn(52788)

Question 1143535: In a GP 1,2,4,..,256 how many terms are there?
Click here to see answer by Alan3354(69443)

Question 1143590: given a and b, suppose that three numbers are inserted between them so that the five numbers form a geometric sequence. if the product of the three numbers between a and b is 27, show that ab is equal to 9.
Click here to see answer by ikleyn(52788)

Question 1143616: I need to create a sequence using this rule: "Adding 3 then subtracting 4" Give five possible answers for the sequence
Click here to see answer by Edwin McCravy(20056)

Question 1143617: Complete the sequence of following number?
7/8,2/3,1/2,4/11,1/4,__,__
Click here to see answer by greenestamps(13200)

Question 1143692: I'm supposed to find an explicit formula for a sequence that goes as 0,0,3,3,5,5,7,7,9,9
Is this actually possible?
Click here to see answer by Edwin McCravy(20056)

Question 1143704: 5,6,9,20,__, 414

Click here to see answer by greenestamps(13200)

Question 1143779: 3,13,61,241,721,1441, ?
Click here to see answer by ikleyn(52788)

Question 1143863: what is the next number in this sequence 17,5,23,1,28,35,12,31,7,3,11
Click here to see answer by ikleyn(52788)

Question 1143862: What are two arithmetic means between -1 and -10
Click here to see answer by ikleyn(52788)

Question 1144031: What are two next numbers?
23 15 26 19 75 20 133
Click here to see answer by Alan3354(69443)

Question 1144114: if k+1,2k-1, 3k+1,are three consecutive terms of a geometric progression, find the possible values of the common ratio?
please help me to show the
workings in full.
Click here to see answer by ikleyn(52788)

Question 1144121: Help me please. I do not know where to start.
1. Your doctor prescribes a daily 20 mg dose of a popular allergy medication, No-Drip. Roughly 24 hours after a first dose of the medicine is used, 40% of the No-Drip has been flushed from the body. You take 20 mg of No-Drip once a day. Make a table to show the maximum amount of No-Drip in your system each day for six days. Express each day's amount as a sum. Then, sketch a graph of the maximum No-Drip and the day number for at least fourteen days.
2. Find the partial sum of the first seven terms in the series described in question 1.
3. What do you notice about the graph of the amount of No-Drip in your system over fourteen days? What does this mean in the context of the problem? Confirm your claim analytically.
4. Make a conjecture about the convergence of arithmetic and geometric series.
5. Explore the sequence of partial sums for these three series using tables and graphs. In each case, will the series converge or diverge?
6. Write a formula for the sum of a convergent geometric series with first term t1 and common ratio r, where |r| < 1.
Click here to see answer by ikleyn(52788)

Question 1144174:
Click here to see answer by josgarithmetic(39618)

Question 1144206: 2c. Examine the diagram and explain how it illustrates a value of (n2 + n)/2.
⚫⚫⚫🔴
⚫⚫🔴🔴 (the sizes of the circles don't matter, just the colors)
⚫🔴🔴🔴
2d. Draw a similar diagram to represent for n = 5.
Click here to see answer by greenestamps(13200)

Question 1144231: I have a sequence of 5,11,17,23. I need to know what the number will be for the 100th number in the sequence.
Click here to see answer by math_helper(2461)

Question 1144258: find the fifth term of the binomial expansion (x+y)^7
Click here to see answer by ikleyn(52788)

Question 1144258: find the fifth term of the binomial expansion (x+y)^7
Click here to see answer by Alan3354(69443)

Question 1144408: Question
1. Increasing or Decreasing
2. Next Term In the Sequence
3. Description of pattern
Sequence:
1.5 , 2.75 , 4
Click here to see answer by greenestamps(13200)

Question 1144407: Questions:
!. Increasing or decreasing?
2. Next Term in the Sequence
3. Description of the Pattern
Sequence:
1.5 2.75 4
Click here to see answer by Alan3354(69443)

Question 1144444: 4,5,9,14,23,37
Click here to see answer by richwmiller(17219)

Question 1144444: 4,5,9,14,23,37
Click here to see answer by ikleyn(52788)

Question 1144524: what is the formula for these number sequence
02 05 08 11 16 33 20
02 09 13 14 23 29 37
Click here to see answer by Alan3354(69443)

Question 1144530: find sum to infinity for following sequence
1 , 2/3 , 3/9 , 4/27 , 5/81 , ....

Click here to see answer by Edwin McCravy(20056)

Question 1144590: I am stuck can anyone assist
Use the method of mathematical induction to prove that
1(5) + 2(5)^2 + 3(5)^3 + ... + n(5)^n =(5 + (4n−1)5n+1)/ 16

Click here to see answer by math_helper(2461)

Question 1144603: the 6th and 9th of a GP are 192 and 1536 respectively find the common ratio

Click here to see answer by josgarithmetic(39618)

Question 1144705: The M&M jar has a square base with a length and width of 7 cm and a height of 6.5 cm. What would be the most reasonable UPPER LIMIT for the number of M&M's in the jar of the choices below?
REMINDER: Rectangular Prism Volume = l · w · h
A. 100
B. 10,000
C. 100,000
D. 1,000,000

Is B correct?
The question and the answer choices in the link here: https://prnt.sc/p35p6h
Click here to see answer by greenestamps(13200)

Question 1144719: For a given arithmetic sequence, the 42nth term, a42, is equal to 194, and the 88th term, a88, is equal to 424.
Find the value of the 10th term, a10.

Click here to see answer by ikleyn(52788)

Question 1144809: A student was conducting a study to determine how many loose Gala apples could be packed in different box sizes at the local farmer's market. The average Gala apple had a diameter of 3.5 inches.
Using the collected data above what would be a reasonable rough estimate of a ratio of how many cubic inches per apple?
A. 0.0023 in^3/apple
B. 23.2 in^3/apple
C. 32.1 in^3/apple
D. 43.1 in^3/apple

Is D correct?

The question and the answer choices in the link here: https://prnt.sc/p3m3wb
Click here to see answer by jim_thompson5910(35256)

Question 1144811: Please help me this question

If A,B,C and X,Y,Z are are two arithmetic sequence,then A+x,B+y,C+Z is are arithmetic sequence
Click here to see answer by jim_thompson5910(35256)

Question 1144816: A student number system for a county requires that the student number be 5 characters. The first 3 characters are any single digit number, but no number can repeat and the last 2 characters must be letters, but no letter can repeat. How many unique student numbers are possible?
A. 1,370
B. 131,040
C. 250,000
D. 468,000
Is D correct?
The question and the answer choices in the link here: https://prnt.sc/p3ubbd
Click here to see answer by jim_thompson5910(35256)

Question 1144817: Which size would you see on the box for a new television whose screen measures 36 inches wide by 27 inches high?

A. 9"

B. 45"

C. 50"

D. 63"

Is B correct?
The question and the answer choices in the link here: https://prnt.sc/p3uju0
Click here to see answer by josmiceli(19441)

Question 1144844: If you have changed the tires on your car, the original diameter is 24.5 inches. to a new diameter of 26 inches, how fast are you actually going if your speedometer is reading 53 mph?
A. 50.5 mph
B. 53 mph
C. 56.2 mph
D. 62.8 mph

Is C correct?
The question and the answer choices in the link here: https://prnt.sc/p40r49
Click here to see answer by josmiceli(19441)

Question 1144850: Jason has the following averages in his math class:
Homework avg: 80
Quiz avg: 84
Test avg: 74
Final Exam: 60
If the teacher weights Homework at 20%, Quizzes at 30%, Tests at 40%, and the final exam at 10%, what is Jason's class average?
A. 74
B. 77
C. 79
D. 82
Is B correct?
The question and the answer choices in the link here: https://prnt.sc/p419pz
Click here to see answer by ikleyn(52788)

Question 1144874: The formula for a baseball player's slugging percentage is:

If a player has 58 singles, 24 doubles, 8 triples, and 39 home runs, with 324 At bats. What is the player's slugging percentage?

A. 0.524

B. 0.779

C. 0.883

D. 0.736

Is C correct?
The question and the answer choices in the link here: https://prnt.sc/p48n1a
Click here to see answer by math_helper(2461)

Question 1144877: The aspect ratio of a rectangular shape is it's length divided by it's width (L/W). If the aspect ratio of a chalkboard is 4:3 and the width is 5 in, what is the length of the chalkboard?
A. 6.67 in
B. 9.33 in
C. 12 in
D. 14 in
Is A correct?
The question and the answer choices in the link here: https://prnt.sc/p49szb
Click here to see answer by rothauserc(4718)

Question 1144880: On a residential single lane road there was a wreck that backed up traffic for 5 miles. 80% of the traffic consists of cars and 20% of the traffic consists of trucks. The average distance between vehicles is 3 feet. The average length of a car is 13.5 feet and the average length of a truck is 20 feet. Estimate how many vehicles are stuck in the traffic jam.
(Hint: There are 5280 feet in 1 mile.)
A. 853 vehicles
B. 1510 vehicles
C. 2103 vehicles
D. 2320 vehicles
Is B correct?
The question and the answer choices in the link here: https://prnt.sc/p4af9h
Click here to see answer by ikleyn(52788)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790