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 110183: I cannot find the solution to -5, 10, -15, 20, ....
Click here to see answer by scott8148(6628)

Question 110553: solve the system use the substitution method
2x-y-z=15
4x+5y+2z=10
-x-4y+3z=-20
please help don't understand it
Click here to see answer by ankor@dixie-net.com(22740)

Question 111933: what are the different types of sequence?
Click here to see answer by jim_thompson5910(35256)

Question 112706: Find the sum of the infinite geometric series:
.8+.08+.008
please help! thanks! <3
Click here to see answer by Fombitz(32388)

Question 114295: Find the specified term of each geometric sequence.
t3 = -12
t6 = 96
t9 = ?
Find t9.
So what I did was, tn = t1 * R^n-1
So, I thought I could make t3 the first term and t6 the nth term, to find the common ratio.
96= -12 * R^6-1
96= -12 * R^5
-8 = R^5
Now I'm stuck.
Click here to see answer by scott8148(6628)

Question 114606: Find two consecutive integers such that the sum of 2 times the first integer and 7 times second integer is 88.
Click here to see answer by jgr45(31)

Question 114715: Write the equation of the line that passes through point (6,4) with a slope of 2.
Click here to see answer by MathLover1(20855)

Question 114715: Write the equation of the line that passes through point (6,4) with a slope of 2.
Click here to see answer by TP(29)

Question 115067:
Find the sum of 11 over 2 + 3 5 over eight

Thank You
Alice
Click here to see answer by checkley71(8403)

Question 115066: Find the sum of 11 over 2 + 3 5 over eight
Thank You
Alice
Click here to see answer by stanbon(75887)

Question 115576: I am very frustrated! I am doing a piece of coursework and have discovered a changing difference pattern. Could someone please explain to me how to apply it and simplify it for my own results. I know the algebraic expression for a changing difference sequence is: a + (n-1)d + half(n-1)(n-2)c
a = value of first term in sequence
d = first difference between the first two numbers
c = is the change between one difference and the next
a = 481
d = 600
c = 240
Changing Difference Sequence:

481, 1081, 1921, 3001, 4321 Sequence
600 840 1080 1320 first difference
240 240 240 Second difference
I have tried for several hours to figure it out for my own results but have just got frustrated. I need to solve the nth term formula for this changing difference sequence to move on with my coursework. Thank you so much for any help!

Click here to see answer by stanbon(75887)

Question 116640: Give the recursive formula for the series 4,16,64...
Click here to see answer by Edwin McCravy(20081)

Question 116644: Write the explicit formula for the sequence 3, 12, 48, 192,...
Click here to see answer by scott8148(6628)

Question 116982: This is a homework problem that I cannot seem to solve. It states to:
Find the sum of the first 20 terms of the series
1 + 8 + 64 + 512 + . . .
Can you please help? Thank you in advance.
Click here to see answer by jim_thompson5910(35256)

Question 117027: I need help finding the first three(3) terms of the expansion (a-b)^10.
I have something that does not seem to make sense. I have a^10 + 10a^9 (-b), or a^10 -10a^9b + 45a^8b^2. I am not even sure how I got this or even if it is right. Please help me, again the problem is (a-b)^10 Thanks so much
Click here to see answer by scott8148(6628)

Question 117289: hello unfortunatly I can't figure out this word problem and i REALLY need help!
A Pythagorean fractal tree starts at Stage 1 with a square of side length 1m. At every consecutive stage, an isoceles right triangle and two squares are attached to the last square(s) drawn. Determine the total area at the 10th stage and the 100th stage. Determine the general term and make conclusions.

Click here to see answer by MathLover1(20855)

Question 117570: linear combinations?????
i don't understand any of this i'm not looking for the answer as i know it but i'm looking for step by step help with the work. plus they have added THREE variables now and i didn't even understand two so please help me.
4x + y = -12
2x + 2y = -15? (answer -1.5, -6)then with THREE 2a + b =5c = -21
a + 2b - 2c = -15
a - 4b + c = 18 (answer -1, -4, 3
Click here to see answer by solver91311(24713)

Question 117897: Not even sure i put this under the right heading. (sigh)...i need help please
Subtract -2.3-(-8.8)
a) -11.1
b) 1.3
c) -1.3
d) 6.5
Click here to see answer by Earlsdon(6294)

Question 117897: Not even sure i put this under the right heading. (sigh)...i need help please
Subtract -2.3-(-8.8)
a) -11.1
b) 1.3
c) -1.3
d) 6.5
Click here to see answer by TP(29)

Question 117354: Find the sum of the series
1 + 2x + 3x^2 + 4x^3 ...
I cannot understand how to find the ratio
Like
1 + 2x + 3x^2 + 4x^3 ...
--\/---\/-------\/--------
--2x---1.5x---1.33x
Now what?
Click here to see answer by Edwin McCravy(20081)

Question 120007: How do I find all of the possibilities to combine 56 numbers, when I can only use six at a time? (I.E. 56,55,54,53,52,51 and 1,2,3,4,5,6)
Thanks much : )
Click here to see answer by stanbon(75887)

Question 120037: Find the general term of a sequence whose first four terms are given.
28.)
2, -1,-4,-7,�

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Question 120065:
A bank pays 4% interest on deposits. If you deposit $1,000 how much will be in your account at the ned of six years?
Solve using a geometeric or arithmetic formula for squence or series.
Click here to see answer by checkley71(8403)

Question 120064: A bank pays 4% interest on deposits. If you deposit $1,000 how much will be in your account at the ned of six years?
Solve using a geometeric or arithmetic formula for squence or series.
Click here to see answer by checkley71(8403)

Question 120067: One minute after it is released, a hot air balloon rose 80 feet. In each succeeding minute the balloon rose only 60% as far as it rose in the previous minute. How far will the balloon rise in 6 minutes?
Solve using a geometeric or arithmetic formula for squence or series.
Click here to see answer by Fombitz(32388)

Question 120479: Find a counterexample to show that the following statement is incorrect:
�The sum of any two odd numbers is divisible by 4�

Click here to see answer by stanbon(75887)

Question 120479: Find a counterexample to show that the following statement is incorrect:
�The sum of any two odd numbers is divisible by 4�

Click here to see answer by MathLover1(20855)

Question 121638: State whether each sequence is a geometric sequence. If so, state the common ratio and list the next three terms.
-5, 1, -1/5, 1/25,....
Click here to see answer by checkley71(8403)

Question 121852: State whether sequence is a geometric sequence. If so, state the common ration and list the next three terms.
-8, 16, -32, 64
Click here to see answer by checkley71(8403)

Question 121855: State whether sequence is a geometric sequence. If so, state the common ration and list the next three terms.
-1/4, -1/2, -1, -2
Click here to see answer by checkley71(8403)

Question 121853: State whether sequence is a geometric sequence. If so, state the common ration and list the next three terms.
25, 5, 1, 1/5
Click here to see answer by checkley71(8403)

Question 121850: State whether sequence is a geometric sequence. If so, state the common ration and list the next three terms.
-14, 7, -1, -1/7
Click here to see answer by checkley71(8403)

Question 122229: write an equation for: 4 consecutive numbers, the sum of the first 3 numbers is equal to 54 more than the 4th number
Click here to see answer by tutor_paul(519)

Question 122446: i dont understand the recursive formula? please explain

Click here to see answer by solver91311(24713)

Question 123318: Transpose V = 2R/R-r so that r is the subject
Click here to see answer by chitra(359)

Question 123372: Please put in correct sequence starting from larger number ending in the smaller number:
I said it was in this order:Is this correct:
1) 0.401
2) 0.4013
3) 0.4030
4) 0.4031
5) 0.40101
6) 0.40303
Click here to see answer by praseenakos@yahoo.com(507)

Question 123680: I have worked out the answer to the question but cannot explain the logic to my 9 year old son. His teacher has explained how to do it. Can you please help. The sum of two numbers is 147. The difference between the two numbers is 43. What are the two numbers.
Click here to see answer by nadinadan(32)

Question 123866: If the average (arithmetic mean) of 5 consecutive integers is 12, what is the sum of the least and greatest of the 5 integers?
5 numbers (x1,x2, x3, x4, x5)=60
x=
Click here to see answer by solver91311(24713)

Question 124994:
the sum of two numbers is 20 and the sum of their square is 208. find these numbers
Click here to see answer by checkley71(8403)

Question 124995: find two consecutive numbers whose product is 72
Click here to see answer by nadinadan(32)

Question 124996: find two numbers consecutive pairs whose product is 80
Click here to see answer by checkley71(8403)

Question 125006: find two consecutive numbers whose product is 72
Click here to see answer by checkley71(8403)

Question 125006: find two consecutive numbers whose product is 72
Click here to see answer by josmiceli(19441)

Question 126386: Tori and Peyton played a number quessing game. Tori thought of 2 numbers and said, " The sumof the numbers is 43 and the difference of the numbers is 9." What 2 numbers was Tori thinking of?
Click here to see answer by stanbon(75887)

Question 126680: determine the common ratio of a geometric sequence whose first term is 2 and whose fourth term is 16?

Click here to see answer by praseenakos@yahoo.com(507)

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, 11791..11835