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

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Question 1151578: The sum of 37+38+39+40+...+110
Click here to see answer by ikleyn(52788)

Question 1151580: First question :
If P=2+4+6+8+...+104 and Q=6+8+10+12+...+106 are sums of arithmetic sequence, determine which is greater, P or Q, and by how much.
Second Question:
Find a 3 by 3 magic square using the numbers 7,8,9,14,15,16,21,22,and 23.
Third question:
Suppose there is a pile of quarters, dimes, and pennies with a total of $1.07.
a) How much of each coin can be present without being able to make change for a dollar?
b)Explain why $1.19 is the greatest amount of money it is possible to have without being able to make change for a dollar.
Fourth Question:
Find the 100th and nth term for each of the following sequences.
a. 1,5,9,13,...
b.70,120,170...
c.1,3,9....
d.8,8^4,8^7,8^10,...
e.109+7x3^32,109+8x3^32,109+9x3^32,...
Fifth question:
The first figure takes 5 matchstick squares to build, the second takes 11 to build, and the third takes 17 to build.
a) how many matchstick squares will it take to build the 8th figure?
b) how many matchstick squares will it take to build the nth figure?
c) how many matchsticks will it take to build the nth figure?
Last Question:
The first difference of a sequence is the arithmetic sequence 3,5,7,9,11,... Find the first six terms of the original sequence in each of the following cases.
a) the first term of the original sequence is 5.
b) the sum of the first two terms in the original sequence is 7.
c) the fifth term in the original sequence is 39.
THANK YOU SO MUCH FOR YOUR HELP I GREATLY APPRECIATE IT !
Click here to see answer by ikleyn(52788)

Question 1151583: Suppose there is a pile of quarters, dimes, and pennies with a total of $1.07.
a) How much of each coin can be present without being able to make change for a dollar?
b)Explain why $1.19 is the greatest amount of money it is possible to have without being able to make change for a dollar
Click here to see answer by ikleyn(52788)

Question 1151584: Find the 100th and nth term for each of the following sequences.
a. 1,5,9,13,...
b.70,120,170...
c.1,3,9....
d.8,8^4,8^7,8^10,...
e.109+7x3^32,109+8x3^32,109+9x3^32,...
Click here to see answer by ikleyn(52788)

Question 1151581: Hello. I need next number in this sequence. Thanks
5,28,2,3,11,16,33,7,12,2,23,31,1,24,11,6,24,25,7,36,4,28,9,26,23
Click here to see answer by ikleyn(52788)

Question 1151582: Find a 3 by 3 magic square using the numbers 7,8,9,14,15,16,21,22,and 23.
Click here to see answer by Alan3354(69443)

Question 1151381: In the sequence 1,4,5,6,7,8,10,16,18,... each number after the first two is the next number that can be expressed as the sum of two previous numbers in only one way. For example, 10 is included because 6+4=10, and there is no other sum of two other numbers in the sequence that equals 10. The number 15 is not included because both 10+5 and 8+7 equals 15. In a similar sequence that begins with the two numbers 100 and 101, what is the sum of the first ten terms?
Click here to see answer by greenestamps(13200)

Question 1151843: - 4, - 16, - 64, - 256, what is the next number.
You can see that the numbers multiply by 4 each time. so that means. -256*4 = -1,024.
Your Welcome

Click here to see answer by iamjustgooder(2)

Question 1151984: 1.Find the sum of the series.
0.1+0.1+0.001+....

Click here to see answer by ikleyn(52788)

Question 1151985: 1.Find the nth term of.
1, 5/7, 7/15, 9/31,....
Click here to see answer by greenestamps(13200)

Question 1151999: 1.Find the sum of the even integers between -24 and 226, including end numbers.
Click here to see answer by MathLover1(20850)

Question 1151998: 1.Find the sum of 60 terms.
5+5*(1/2)+6+6*(1/2)+....

Click here to see answer by greenestamps(13200)

Question 1152056: find the sum 2+(-6)+18 + ......(-486)

Click here to see answer by MathLover1(20850)

Question 1152056: find the sum 2+(-6)+18 + ......(-486)

Click here to see answer by MathTherapy(10552)

Question 1152069: Given 2;5;8 as a sequence prove that none of the terms are not a perfect
square
Click here to see answer by ikleyn(52788)

Question 6533: Please help me solve
Click here to see answer by Shin123(626)

Question 1151518: The first figure takes 5 matchstick squares to build, the second takes 13 to build, and the third takes 21 to build, as can be seen by clicking on the icon below.
(a) How many matchstick squares will it take to build the 9th figure?
(b) How many matchstick squares will it take to build the nth figure?
(c) How many matchsticks will it take to build the nth figure?

Thank you for your help
Click here to see answer by Shin123(626)

Question 6529: Please help me solve

Click here to see answer by Shin123(626)

Question 1126254: Find the common ratio and write out the first four terms of the geometric sequence 9^n+3/10?
Click here to see answer by Shin123(626)

Question 1152187: A quadratic pattern has a second term equal to -1,a third equal to -6 and a fifth term equal to -14.Calculate the second difference of this quadratic pattern.
Hence,or otherwise ,calculate the first term of the pattern.

Click here to see answer by MathLover1(20850)

Question 1152190: 1,1,1,3,5,9,17,31 find the 2019th member of this sequence

Click here to see answer by MathLover1(20850)

Question 1152227: The nth term of 10,8,6,4,2,0
Click here to see answer by MathLover1(20850)

Question 1152227: The nth term of 10,8,6,4,2,0
Click here to see answer by MathTherapy(10552)

Question 1152227: The nth term of 10,8,6,4,2,0
Click here to see answer by ikleyn(52788)

Question 1152504: I need to find the solution for the following sequence:
2,3,4,7,8,11,?
Click here to see answer by ikleyn(52788)

Question 1152504: I need to find the solution for the following sequence:
2,3,4,7,8,11,?
Click here to see answer by greenestamps(13200)

Question 1152599: The 16th of and A.P is 88 given that it's common difference is 5 find the first term & 28th term
Click here to see answer by josgarithmetic(39618)

Question 1152636: convert 123y=83 base 10

Click here to see answer by Alan3354(69443)

Question 1152636: convert 123y=83 base 10

Click here to see answer by greenestamps(13200)

Question 1152843: 72, 110, 158, 220, 317, 440, 634, 880 ?
Click here to see answer by Alan3354(69443)

Question 1152843: 72, 110, 158, 220, 317, 440, 634, 880 ?
Click here to see answer by greenestamps(13200)

Question 1152869: Consider the sequence of numbeer: 2;5;2;9;2;13;2;17
Calculate the sum of the first 100 terms of the sequence
Click here to see answer by greenestamps(13200)

Question 1152960: find the possible values of p if p-3,3p-5,18-5 are consecutive terms of a geometric progression.
Click here to see answer by MathLover1(20850)

Question 1152960: find the possible values of p if p-3,3p-5,18-5 are consecutive terms of a geometric progression.
Click here to see answer by ikleyn(52788)

Question 1153077: https://media.educationgalaxy.com/content/Images/Questions/doreen@educationgalaxy.com/image--480079904.jpg
Click here to see answer by ikleyn(52788)

Question 1153131: Hello! I've been trying to solve this problem- it goes as shown: For a particular sequence, each term is the sum of the three preceding terms. If a, b, c, d, e, 0, 1, 2, 3 are consecutive terms of this sequence, what is the value of a + b + c + d + e?
My attempts to solve this have gone as follows:
Since the 8th term (2) is the sum of e + 0 + 1, e must be 1, as that would be the only solution to this. I worked backwards from there: 1 = 0 + 1 + d, so d must be 0. This is where my reasoning failed. I thought c was equal to -1, which meant that b must be 2, and a must be -1. However, since the only term preceding b is -1, I thought b must be -1, too.
Is it wrong of me to think the sequence must start on a? Is it implied that the sequence goes much further backwards?
Thank you in advance for any and all help!
Click here to see answer by math_helper(2461)

Question 1153200: Consider the arithmetic series 3+7+11+15+19+23+27+...and answer the questions which fo.
(a) T1= S1=
(ii) express T1 in terms of S1
(b) T2= S2=
(ii)Express T2 in terms of S2 and S1
Click here to see answer by ikleyn(52788)

Question 1153231: 1,8,2,7,6,4,1,2,5,2,1,6,3,4,3,5,1,2,7,2,9,1,0,0,0,1,3,3,1,1,7,2,8 What’s the next four numbers in the sequence?
Click here to see answer by greenestamps(13200)

Question 1153229: how many rows are in the corner section of a tennis court stadium containing 255 seats if the first row has a 12 seats and the each successive row has 3 additional seats
Click here to see answer by greenestamps(13200)

Question 1153267: what is the next 4 digits of this sequence?
182764125216343512729100013311728
Click here to see answer by ikleyn(52788)

Question 1153267: what is the next 4 digits of this sequence?
182764125216343512729100013311728
Click here to see answer by greenestamps(13200)

Question 1153337: Find the sum of the series ∑12i=1(3i−1)
Click here to see answer by greenestamps(13200)

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