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 1111838: A function is defined by f(x)= square root of (2x+5). What is f^-1(x), the inverse of f(x)?
Click here to see answer by josgarithmetic(39618)

Question 1111836: What is the 100th term of the pattern 3a-4b, 4a-2b, 5a, 6a+2b, 7a+4b,....

Click here to see answer by ikleyn(52788)

Question 1111789: Given sinθ, 2 cosθ and 2 sinθ are three consecutive terms in an arithmetic sequence. Find the value of θ in radians given θ is an acute angle.
Click here to see answer by greenestamps(13200)

Question 1112026: 3-6,12,4,20?
Click here to see answer by ikleyn(52788)

Question 1112161: find the sum of first 10 terms for the series of -1 , -8 , -27 , -64 , ....
Click here to see answer by Fombitz(32388)

Question 1112218: Please help me work out this algebra problem in series. There is an infinity symbol on top of sigma n=1 below sigma. Then to the right of the sigma -4(1/3)^(n-1).
A.)the first 4 terms in the series.
B.)Does the series diverge or converge?
C.)Find the sum of the series if it has a sum.
I do not think there is a sum, and I'm pretty sure it converges. I am having a really hard time with these infinite geographic series. Thank You for your help.
Click here to see answer by ikleyn(52788)

Question 1112301: The number of visitors to a website in the first week is 50. The number of visitors each week is double the number of visitors the previous week. What is the total number of visitors to the website in the first 8 wk?

Click here to see answer by ikleyn(52788)

Question 1112306: Peter works for a house building agency for 4 months per year. He starts out making $3000 per month. At the end of the each month, his salary increases by 5%. How much money will he make in those 4 months?

Click here to see answer by josgarithmetic(39618)

Question 1112373: How much does -3 exceed -10
Click here to see answer by Boreal(15235)

Question 1112393: Which is larger,the 10th term of an arithmetic sequence that begins with the term 0and 100 or the 10th term of a geometric sequence that begins with the terms 5 and 10?show work that justifies your answer
Click here to see answer by ikleyn(52788)

Question 1112391: A geometric sequence is defined using the following rule
f(0)=4 and f(n)=f(n-1).-2
Find the fourth term of the sequence.show how you arrived at your answer
Click here to see answer by stanbon(75887)

Question 1112424: Q: 5, 6.5, 9, 14, x
Find x.
A. 15
B. 20
C. 21
D. 29
Click here to see answer by ikleyn(52788)

Question 1112424: Q: 5, 6.5, 9, 14, x
Find x.
A. 15
B. 20
C. 21
D. 29
Click here to see answer by Alan3354(69443)

Question 1112506: what is the missing number in this sequence?
5, ,10,12 1/2
Click here to see answer by ikleyn(52788)

Question 1112554: sum of infinite gp is 2 and sum of their cubes of the terms is 8/7 find gp
Click here to see answer by math_helper(2461)

Question 1112775: given that the sum of the first two terms of a geometric progression is 90 and the sum to infinity is 640/7,find the two possible values of the common ratio
Click here to see answer by ikleyn(52788)

Question 1112803: the sum and product of the three numbers in a Geometric progression are 28 and 512 respectively. what are the three numbers
Click here to see answer by stanbon(75887)

Question 1112814: the 3rd and 7th term of an arithmetic progression are 18 and 30 respectively, the sum of the first 33 terms is?
Click here to see answer by greenestamps(13200)

Question 1112832: In a certain geometric sequence, t sub3 = 400 and t sub5 = 25. What could the value of t sub8 be?
Click here to see answer by solver91311(24713)

Question 1112832: In a certain geometric sequence, t sub3 = 400 and t sub5 = 25. What could the value of t sub8 be?
Click here to see answer by greenestamps(13200)

Question 1112816: using De'moivres method evaluate sin5theta/sin theta and leave your answer in cosine
Click here to see answer by ikleyn(52788)

Question 1112962: Please help me. 2p+3, 4p+3, and 5p+2 are the first three terms in an arithmetic sequence. How to find p?
Thank you.
Click here to see answer by ikleyn(52788)

Question 1112962: Please help me. 2p+3, 4p+3, and 5p+2 are the first three terms in an arithmetic sequence. How to find p?
Thank you.
Click here to see answer by rothauserc(4718)

Question 1112961: Can someone help me with this? Thank you.
infinite geometric series a+ar+ar^2+ar^3+... converges to 10, and the terms involving the even powers of r converges to 6. What is the value of a+r?
Click here to see answer by rothauserc(4718)

Question 1112959: Please help. How to write sigma notation : 3-5x+7x^2-9x^3+...-65x^31
Thank you.
Click here to see answer by solver91311(24713)

Question 1112969: 7, 16, 8, 27, 9,
Click here to see answer by ikleyn(52788)

Question 1113142: Were is this number series from: 4, 7, 11, 14, 23, 27, 35, 39, 51, 64, 70, 85, 93, 99, 108, 127, 141, 147, 165, 175, 181, 197, 209, 227, 249, 256, 257, 266 ?

Click here to see answer by ikleyn(52788)

Question 1113166: Calculate the following in hexadecimal and identify which one of the following options gives the correct octal answer.
FACE + DEAF
AD97D
1D97D
16755
16575
So, I determined that the hex values are 57007 and 64206
I added these figures together, getting 121213.
I then tried to apply the octal system to this:

giving me 354335, which seems dramatically wrong
Click here to see answer by Theo(13342)

Question 1113177: what is the next number and how to solve it
7, 14, 14, 0, -28, -56
thanks a lot
Click here to see answer by Alan3354(69443)

Question 1113195: please help me to find a pattern in the sequence :
3 , 13 , 19 , 26 , 33 , 44
Click here to see answer by Alan3354(69443)

Question 1113178: what is the next number and how to solve it
7, 14, 14, 0, -28, -56
thanks a lot
Click here to see answer by greenestamps(13200)

Question 1113255: What is the solution to this number series: 4, 7, 11, 14, 23, 27, 35, 39, 51, 64, 70, 85, 93, 99, 108, 127, 141, 147, 165, 175, 181, 197, 209, 227, 249, 256, 257, 266 ? I think it's connected to the prime numbers.
Thank you!

Click here to see answer by ikleyn(52788)

Question 1113175: What is the solution to this number series: 4, 7, 11, 14, 23, 27, 35, 39, 51, 64, 70, 85, 93, 99, 108, 127, 141, 147, 165, 175, 181, 197, 209, 227, 249, 256, 257, 266 ? I think it's connected to the prime numbers.
Thank you!
Click here to see answer by ikleyn(52788)

Question 1113344: please help complete the sequence
62;31;94;47;142;71;214
Click here to see answer by ikleyn(52788)

Question 1113448: WHATS THE MISSING number in this sequence:
4,16,64,___,1024 ?

Click here to see answer by josgarithmetic(39618)

Question 1113448: WHATS THE MISSING number in this sequence:
4,16,64,___,1024 ?

Click here to see answer by greenestamps(13200)

Question 1113585: What is the next number in the sequence 7, 16, 8, 27, 9

Click here to see answer by josgarithmetic(39618)

Question 1113582: What is the next number in the sequence 3, -6, 12, 4, 20?

Click here to see answer by Alan3354(69443)

Question 1113582: What is the next number in the sequence 3, -6, 12, 4, 20?

Click here to see answer by ikleyn(52788)

Question 1113698: Barbara makes 20 bracelets during the first week to sell at next years craft fair. Each week she nakes 6 braceltes more than the previous week. Write an exponential formula for this sequence.
Click here to see answer by ikleyn(52788)

Question 1113759: The sum of the series 1/√3+1+3/√3+........... To 18 terms is ??

Click here to see answer by KMST(5328)

Question 1113863: The first three consecutive terms of an exponential sequence are (x-1), 2x and (5x+3) respectively. 1.find the value of x. 2.find the common ratio. 3.find the sum of the first six terms.
Click here to see answer by greenestamps(13200)

Question 1114197: Find the sum of n terms of a G.P. whose nth term is 3(2)^n-1
Click here to see answer by amalm06(224)

Question 1114197: Find the sum of n terms of a G.P. whose nth term is 3(2)^n-1
Click here to see answer by ikleyn(52788)

Question 1114196: If a, b, c are in A.P, then prove that
(i)
(ii)
(iii)
are also in A.P.
(PLEASE SOLVE ALL THE PARTS. I AM THANKFULL)
Click here to see answer by richwmiller(17219)

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