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 735081: help me to find the sum 3+11+19+...+787.
Click here to see answer by stanbon(75887)

Question 734425: What is the next term in the sequence below?
1,7,25,61,121,____
Why does my answer make sense?
Click here to see answer by Edwin McCravy(20056)

Question 735082: The sum of 3 numbers in an A.P is 21 and their product is 280. find the numbers

Click here to see answer by mananth(16946)

Question 735172: what is the next term for 12 24 36 60 96

Click here to see answer by MathLover1(20850)

Question 735581: sum of (1)+(2*2)+(3*3*3)+(4*4*4*4)+(5*5*5*5*5)+..............till n rise to power n
Click here to see answer by MathLover1(20850)

Question 736265: find the sum of the first 328 even natural numbers
Click here to see answer by Alan3354(69443)

Question 736265: find the sum of the first 328 even natural numbers
Click here to see answer by solver91311(24713)

Question 736363: Is 12,40,68,96 sequence geometric or arthmetic? If possible what is the common ratio or difference

Click here to see answer by MathLover1(20850)

Question 736406: 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.
Click here to see answer by mananth(16946)

Question 736833: Determine a formula for the geometric sequence that begins 1.1, 3.3, 9.9. What is the 10th term of this sequence?
Click here to see answer by fcabanski(1391)

Question 736885: If your 40 & your boyfriend is 10 then your 1/4 times older than him. In five years you'll be 45 & he will be 15 that means you'll be 1/3 years older than him. In fifteen years you'll be 60 & he'll be 30 you'll be 1/2 years older than him. My question is how many years will it take to be the same age ???, i have no idea if this is algebra ? I neeed help, thanks

Click here to see answer by Alan3354(69443)

Question 736986: What is the next number in the series: 9,73,241,561,1081,1849,...
Click here to see answer by MathLover1(20850)

Question 737093: if x, y, and z are the first three terms of a geometric sequence, show that x^2, y^2 and z^2 form another geometric sequence
Click here to see answer by mananth(16946)

Question 737194: Evaluate the infinite geometric series. Round to the nearest hundredth if necessary.
50 + 10 + 2 + ...
Click here to see answer by jim_thompson5910(35256)

Question 737267: Hey, I am confused with this word problem in which I have to use arithmetic/geometric sequences.
How many ancestors from parents to great-great-great-great grandparents do you have?

Thank you! :)
Click here to see answer by jim_thompson5910(35256)

Question 737276: Hello! I am confused on how to solve this problem in which I have to solve using geometric/arithmetic sequences.
For each of the first 12 years of its fruitful life a certain apple tree is expected to produce 8 more apples than it had the preceding year. If the tree produces 17 apples the first year, how many apples can the tree be expected to produce during the 12th year?
Thanks! :)
Click here to see answer by reviewermath(1029)

Question 737274: Hey! I am confused on how to solve this problem in which I have to solve by using geometric/arithmetic sequences.
Your work at a job that paid wages of $1 the first day, $2 the second day, $4 the third day, with your earnings doubling each successive day. What are your total earnings after working 14 days?
Thanks! :)

Click here to see answer by MathLover1(20850)

Question 737273: Hello! I am confused with this word problem in which I have to use geometric/arithmetic sequences.
In a certain school system, the starting salary for a teacher is $24,000 with an annual raise of $1200 each year until a maximum salary of $40,800 is reached. How many years must a person teach to reach the maximum salary?
Thanks!:)
Click here to see answer by rfer(16322)

Question 737272: Hello! I am confused with this word problem in which I have to use geometric/arithmetic sequences.
In January of a certain year, Will deposited $120 in his savings account. For each subsequent month of the same year and each month of the following year, his monthly deposit increased by $5. How much did he deposit in the savings account altogether during the 2 years?
Thanks! :)
Click here to see answer by josgarithmetic(39618)

Question 737367: 1 2 3 5 ? 13 21 ?
Click here to see answer by sachi(548)

Question 737674: Hey! I have a question on how to solve this. I have to use geometric/arithmetic sequences in order to solve this word problem.
A farmer gathers 35 bushels of potatoes on the first day of harvest. The farmer estimates that on each successive day of the harvest, the amount gathered can be 4 bushels more that the preceding day. If the harvest lasts 14 days, what is the total number of bushels harvested?
Thanks! :D
Click here to see answer by mananth(16946)

Question 738402: 12 is 4% of what number
Click here to see answer by checkley79(3341)

Question 738574: 7
∑ 2k/3
k=1
Hard to type this question. The 7 is above and the k=1 below the sigma

Click here to see answer by MathLover1(20850)

Question 738573: 6
∑ (-1)^n *5n
n=3
Hard to type this question. The 6 is above and the n=3 below the sigma

Click here to see answer by MathLover1(20850)

Question 738572: 7
∑ 2k/3
k-1
Hard to type this question. The 7 is above and the k=1 below the sigma

Click here to see answer by MathLover1(20850)

Question 738790: In a sequence of numbers each term after the first three terms is the sum of the previous three terms. The first three terms are -3, 0, 2. What is the first term to reach 100? I would also like to know the equation for the nth term.
Click here to see answer by fcabanski(1391)

Question 738254: 1,2,0.5,5,0.25,8..... Calculate the sum of 100 terms of the sequence
Click here to see answer by Edwin McCravy(20056)

Question 739087: 1-An aritmetic sequence has its 5th term equal to 22 and its 15th term equal to 62.Find its 100th term.
2-Find the sum of the first 50 even positive integers.
Click here to see answer by reviewermath(1029)

Question 739449: How do I solve this problem?..To reproduce, a single bacterium splits into two. Assume it takes a single bacterium 20 min to split. When will there be 128 bacteria?
Click here to see answer by richwmiller(17219)

Question 739490: √(8+√38+√57+√108+√1)=??

Click here to see answer by jam123(18)

Question 739565: Insert 3 arithmetic means between -19 and 79. (common difference)
Use a formula and show your work. Hint: This is an arithmetic progression with 5 terms, so n=5, hint: find d then add etc.
-19, _____, _____, _____, 79

Click here to see answer by josgarithmetic(39618)

Question 739620: general term formula for 1 5 14 28 47 please help me

Click here to see answer by jim_thompson5910(35256)

Question 739620: general term formula for 1 5 14 28 47 please help me

Click here to see answer by MathLover1(20850)

Question 739888: If the first term of the arithmetic sequence is 5 and the ninth term is 29, where would the number 101 be found?
Click here to see answer by josgarithmetic(39618)

Question 739965: the sum of 4 term of an A.p is 4 and the sum of the product of the first and the last and the 2 middle term is -3 find the numbers??
Click here to see answer by mananth(16946)

Question 739966: find the sum of all natural numbers between 1 and 100 which are not exactly divisible by 2 or 3?
Click here to see answer by KMST(5328)

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 Ed Parker(21)

Question 741042: Find the sum of the arithmetic sequence.
6+3.5+1-1.5-4-...-49
Click here to see answer by reviewermath(1029)

Question 741827: Is there a formula to solve this question....The population of a community was 82,000 at the beginning of 2000. Assuming a rate of growth of 1.6% per year since 2000, what will be the population be at the beginning of 2025?
I can manually get the answer but would rather use a formula. Is there one that will work? I can't seem to get the formulas that I know to work.
Click here to see answer by KMST(5328)

Question 742223: 8th term of geometric sequence with the first term of -2 and the fifth term -512
Click here to see answer by josgarithmetic(39618)

Question 742500: how do I solve and graph f(x)= -2x+3
Click here to see answer by lwsshak3(11628)

Question 742502: Determine the number of terms in the arithmetic series:
a1=10
an=74
sn=378
Click here to see answer by MathLover1(20850)

Question 742611: What is Sn for the arithmetic series with d=-4, an=27, and n=9
a.360
b.387
c.418
d.451
Click here to see answer by mananth(16946)

Question 742905: Find all numbers whose sum when added to its multiplicative inverse is 13/7
Click here to see answer by stanbon(75887)

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