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 1210576: Finish the sequence 3. 6. 18 ___
which of these numbers is correct
84
60
72
30
Click here to see answer by josgarithmetic(39736)

Question 1210576: Finish the sequence 3. 6. 18 ___
which of these numbers is correct
84
60
72
30
Click here to see answer by KMST(5337)

Question 1210575: Finish the sequence 3. 6. 18 ___
which of these numbers is correct
84
60
72
30
Click here to see answer by math_tutor2020(3832)

Question 1210552: Pls help me and solve this sequence:
The first and the third terms of a G.P are 5 and 80 respectively. find the 4th term
Click here to see answer by greenestamps(13296)

Question 1210536: Find the sum of first 100 terms
Click here to see answer by CPhill(2189)

Question 1204431: Determine whether 280 is a term in the G.P 1,3,9,27…
Click here to see answer by ikleyn(53618)

Question 1130236: Lauren is planning to raise her batting average. When she set up her weekly practice schedule, her batting average was 250. Lauren intends to increase her batting average by 5 each week. Find a pattern and write a formula that will give her expected batting average after n weeks.
a1 =
d=
Using the formula, how many weeks will Lauren need to practice if she expects to earn a batting average of 300?
Click here to see answer by n2(54)

Question 1146477: Jenny puts aside $20 at the end of each month for 3 years. How much will she have then of the investment earns 8.2% p.a., paid monthly?
Click here to see answer by ikleyn(53618)

Question 729526: Hi how would you write the equation for the following question?
A 7kW, 240V generator is installed in a photovoltaic system designed with two days of battery storage at 50% depth of discharge(the load uses 50% of the battery storage over 2 days) and the system is sized for a charging rate of C/10.(C/10 = 100% charged over 10 hours C/20 would be 100% charged over 20 hours, etc) Approximately how much fuel will be required per day when the generator is the only power source? The generator burns about 1.6 gallons per hour.
I know the answer is 4 gal per hr.
I would like to see how to write the equation then solve it.
Thank You for your help
Bob
Click here to see answer by ikleyn(53618)

Question 732177: After touchdown, a landing aircraft travels 200 feet the first second, 160 feet the next second, 121 feet the third second, and so on. How many feet will the plane travel in 10 seconds?
Click here to see answer by ikleyn(53618)

Question 733276: 10 = 1/5 a + 2 solve the equation for a?
Click here to see answer by ikleyn(53618)

Question 740508: Determine the common ratio of a geometric series that has these partial sums: S4= -3.5, S5= -3.75, S6= -3.875.
I am having a lot of problems trying to find the common ratio. This is a multiple question and none of the answers fit.
Click here to see answer by ikleyn(53618)

Question 1210418: If (3-x)+(6)+(7-5x) is a geometric series,find two possible values for
a) x
b)the common ratio
c)the sum of the Gp
pls show workings
Click here to see answer by greenestamps(13296)

Question 488218: The sum of all terms of an infinite geometric progression is 12, and each term is three times the sum of all terms that follow it. What is the first term of the sequence?
Please help. I'm not sure if I'm following it correctly but here's what I've got so far:
Formula: S(infinity)=a1/1-r
where,
S(infinity)=12
a1=3(a2+a3+a4+..an)
And that's about it. I don't know what to do afterwards. :(
Click here to see answer by ikleyn(53618)

Question 552039: If a ball rebounds three-fifths as far as it falls, how far will it (vertically) travel before coming to rest if dropped 14 feet?
Click here to see answer by ikleyn(53618)

Question 1210386: 1, 2, 0, 3, -1, 4, -2
Please enter integer sequence
Click here to see answer by AnlytcPhil(1810)

Question 1210386: 1, 2, 0, 3, -1, 4, -2
Please enter integer sequence
Click here to see answer by mccravyedwin(419)

Question 1210386: 1, 2, 0, 3, -1, 4, -2
Please enter integer sequence
Click here to see answer by Edwin McCravy(20077)

Question 1210385: 1, 2, 4, 8, 16, 32
Please enter integer sequence
Click here to see answer by mccravyedwin(419)

Question 1210385: 1, 2, 4, 8, 16, 32
Please enter integer sequence
Click here to see answer by Edwin McCravy(20077)

Question 1169051: The sample of work produced by lathe is 10000.
a. If the machine doubled this production every 20 minutes, how much will it produce
in one hour?
b. How long will it take the machine to produce 8 million?
Click here to see answer by ikleyn(53618)

Question 1210345: THE 2ND AND 7TH TERM OF A G.P ARE 18 AND 4374 RESPECTIVELY. FIND THE
1) COMMON DIFFERENCE
2) FIRST TERM
3) SUM OF THE 4TH AND 8TH TERM
4) SUM OF THE FIRST 10 TERMS
Click here to see answer by AnlytcPhil(1810)

Question 1209826: For a positive integer k, let
S_k = 1 \cdot 1! \cdot 2 + 2 \cdot 2! \cdot 3 + \dots + k \cdot k! \cdot (k + 1).
Find a closed form for S_k.
Click here to see answer by ikleyn(53618)

Question 1209827: Find a closed form for
S_n = 1! \cdot (1^2 + 1) + 2! \cdot (2^2 + 2) + \dots + n! \cdot (n^2 + n).\]
for any integer n \ge 1. Your response should have a factorial.
Click here to see answer by ikleyn(53618)

Question 1209805: Let a_1 + a_2 + a_3 + dotsb be an infinite geometric series with positive terms. If a_2 = 10, then find the smallest possible value of
a_1 + a_2 + a_3.
Click here to see answer by ikleyn(53618)

Question 1179819: f. Find the present values of the following annuities
i. RM6,000 every year for 8 years at 12% compounded annually
ii. RM800 every month for 2 years 5 months at 5% compounded monthly

Click here to see answer by ikleyn(53618)

Question 1210233: Show that the sum of n terms of the progression
log(x), log(x^2), log(x^3), log(x^4) , ..., log(x^n) is (n*(n+1)/2)*log x.
Click here to see answer by mccravyedwin(419)

Question 1210233: Show that the sum of n terms of the progression
log(x), log(x^2), log(x^3), log(x^4) , ..., log(x^n) is (n*(n+1)/2)*log x.
Click here to see answer by ikleyn(53618)

Question 1210233: Show that the sum of n terms of the progression
log(x), log(x^2), log(x^3), log(x^4) , ..., log(x^n) is (n*(n+1)/2)*log x.
Click here to see answer by Edwin McCravy(20077)

Question 1168274: what is the first five terms and 50th term of this sequence.
An=2a n-1 + 5 and a1=3
Click here to see answer by Edwin McCravy(20077)

Question 1168274: what is the first five terms and 50th term of this sequence.
An=2a n-1 + 5 and a1=3
Click here to see answer by greenestamps(13296)

Question 1168274: what is the first five terms and 50th term of this sequence.
An=2a n-1 + 5 and a1=3
Click here to see answer by ikleyn(53618)

Question 1210209: If a,b,c are in Harmonic Progression, show that 1/a + 1/(b+c) , 1/b + 1/(c+a) , 1/c + 1/(a+b) are also in Harmonic Progression
Click here to see answer by CPhill(2189)

Question 1210195: If a,b,c are in Harmonic Progression,prove that 1/a + 1/(b+c), 1/b + 1(c+a), 1/c + 1(a+b) are also in Harmonic Progression
Click here to see answer by mccravyedwin(419)

Question 1168320: Suppose the yearly inflation rate from 2014 to 2020 is 15%, the table that costs $800 at the start of 2014 costs $920 at the start of 2020, and so on. What equation represents the cost of the table from the year 2014 to 2020?
Click here to see answer by ikleyn(53618)

Question 1209977: For a positive integer n, let f(n) denote the integer that is closest to
. Find the integer m so that
.

Click here to see answer by Edwin McCravy(20077)

Question 1209977: For a positive integer n, let f(n) denote the integer that is closest to
. Find the integer m so that
.

Click here to see answer by ikleyn(53618)

Question 1209905: Fill in the blanks, to make a true equation.
3/(3^2 - 1) + 3^2/(3^4 - 1) + 3^3/(3^6 - 1) + 3^4/(3^8 - 1) + ... + 3^(2(n - 1))/(3^(2n) - 1) = ___/___

Hint: Let S_n = \frac{3}{3^2 - 1} + \frac{3^2}{3^4 - 1} + \frac{3^3}{3^6 - 1} + \frac{3^4}{3^8 - 1} + ... + \frac{3^{2(n - 1)}}{3^{2n} - 1}. Compute the first few values of S_n.
Click here to see answer by ikleyn(53618)

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