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 1102305: the sum of the first nth term of the series where the r term is a 21-3r how many terms must be taken for the sum to be zero
Click here to see answer by greenestamps(13200)

Question 1102432: a colony of insects was found to have 250 insects at the beginning. thereafter the number of insects doubled every 2 days. find how many insects there were after 16 days?
Click here to see answer by josgarithmetic(39617)

Question 1102282: is there a pattern that repeats or a way to predict next number in this string: 2,3,5,9,2,6,12,2,12,10,2,9,1,11,4,5,12,11,8,8,5,8,8,12,9,7,12,1,10,1,2,6,13,2,2,11,3,2,12,2,3,9,7,10,13,12,10,12,k,10,1,9,13,5,4,11,10,4,8,10,12,12,7,9,5,12,5,7,12,3,6,1,12,2,2,4,3,6,9,12,12,1,10,8,4,4,11,12,11,10,10,5,10,8,8,7,7,8,2,3,1,10,9,3,9,12,13,10,1,1,5,10,4,5,8,10,5,13,5,4,13,1,12,8,2,8,12,12,10,11,8,6,8,5,6,8,1,11,9,13,1,9,4,10,7,12,7,11,11
Click here to see answer by greenestamps(13200)

Question 1102476: The 5th term in a sequence is 25, and each term is 3 less than the previous term. Write an explicit rule and a recursive rule to describe the sequence.
Click here to see answer by KMST(5328)

Question 1102600: Having a discussion about this sequence
1, 1, 2, 15, 104, 695
In my opinion, next numbers are 2885, 8571, 20219 etc.
But he argues that it is 5004 instead of 2885.
Who is right? Thanks!
Click here to see answer by greenestamps(13200)

Question 1102528: lim( n->infinity) U( n) for the sequence 1/2, 1/4, 1/6, 1/8
Click here to see answer by Edwin McCravy(20056)

Question 1102616: Find three consecutive terms of an arithmetic sequence, if the sum of the first and second terms is 30, and if the product of the first and third terms is 153.
Click here to see answer by Edwin McCravy(20056)

Question 1102630: 966,485,874,796,739,212,411,346,623
what are the next three numbers in the series aand how can i solve this?
Click here to see answer by greenestamps(13200)

Question 1102633: Kendal is stacking boxes that are 7.5 inches tall.
I figured that I can multiply 7.5 by the amount of boxes he is stacking to know the height of all the boxes stacked.
But, what would be the 4th term of the sequence if the sequence is defined by the rule f(n)=the height(in inches) of n boxes.
Click here to see answer by ikleyn(52787)

Question 1102883: How many terms must be added in an arithmetic sequence whose first term is 1919 and whose common difference is 66 to obtain a sum of 4012?
Click here to see answer by josgarithmetic(39617)

Question 1102887: How many terms must be added in an arithmetic sequence whose first term is 19 and whose common difference is 6 to obtain a sum of 4012?
Click here to see answer by josgarithmetic(39617)

Question 1102884: A mosaic is designed in the shape of an equilateral triangle, 12 feet on each side. Each tile in the mosaic is in the shape of an equilateral triangle, 12 inches to a side. The tiles are to alternate in color as shown in the illustration. How many tiles of each color will be required?
Click here to see answer by Fombitz(32388)

Question 1102910: The recursive rule for a sequence is f(1)=8 1/2, f(n)=f(n-1)-1/2.
How should I find the explicit rule?
Click here to see answer by Edwin McCravy(20056)

Question 1103118: What is the indicated term for this sequence?
5n squared(7n-100);a(14)
a(14)=
Click here to see answer by greenestamps(13200)

Question 1103117: Find the sum of the first 24 terms of the arithmetic series.
1+8+15+22+...
S(24)=
Click here to see answer by greenestamps(13200)

Question 1103120: Find a 1 when d equals=−3 and a 9=3.
a 1=
I really don't want to screw this problem up as when I do these problems I am usually off by a couple of whole numbers I need an exact correct answer please so I don't get the wrong answer.
Click here to see answer by ikleyn(52787)

Question 1102909: The explicit rule for a sequence is f(n)=1.25(n-1)+6.25.
What should I do to find the recursive rule?
Click here to see answer by robertb(5830)

Question 1103432: Find the common ratio of a finite geometric series if the first term is 11, and the sum of the first 12 terms is 2922920.
Click here to see answer by greenestamps(13200)

Question 1103432: Find the common ratio of a finite geometric series if the first term is 11, and the sum of the first 12 terms is 2922920.
Click here to see answer by ikleyn(52787)

Question 1103369: Determine if the limit exists as n goes to infinity:
+...+ .
If the limit exists then find its value.
Click here to see answer by math_helper(2461)

Question 1103556: In an arithmetic sequence, the third term is 1 and the ninth is 49. What is the explicit formula for the sequence?
Click here to see answer by greenestamps(13200)

Question 1103956: How do you find the nth term of the geometric sequence whose initial term and common ratio are: a1 = -6 , r = -4
Click here to see answer by ikleyn(52787)

Question 1103960: What will be the sum of 3+7+11+15+19 ________ upto 80 terms
Click here to see answer by greenestamps(13200)

Question 1103960: What will be the sum of 3+7+11+15+19 ________ upto 80 terms
Click here to see answer by ikleyn(52787)

Question 1103965: The L.C.M. of 5/7, 10/9 and 15/11 will be .......
Click here to see answer by Edwin McCravy(20056)

Question 1103965: The L.C.M. of 5/7, 10/9 and 15/11 will be .......
Click here to see answer by ikleyn(52787)

Question 1103995: For an arithmetic sequence a₁₃ = 241 and common difference = 7. Determine the explicit formula and the first five terms of the sequence
Click here to see answer by Edwin McCravy(20056)

Question 1104072: resining
l:50::c:?
Click here to see answer by josgarithmetic(39617)

Question 1104076: L : 50 :: C : ?
Click here to see answer by ikleyn(52787)

Question 1104076: L : 50 :: C : ?
Click here to see answer by Edwin McCravy(20056)

Question 1104086: ab(x^2+y^2)-xy(a^2+b^2)
ab+bc+ax+cx
a(a+b-c)-bc

Click here to see answer by richwmiller(17219)

Question 1104112: Find the sum of the series +
Click here to see answer by greenestamps(13200)

Question 1104112: Find the sum of the series +
Click here to see answer by ikleyn(52787)

Question 1104205: Three bells toll together and they begin to toll at intervals 1.6, 2.7 and 1.2 minutes respectively.
Find the number of times the first bells will toll up to the time when three bells toll together again

Click here to see answer by Alan3354(69443)

Question 1104227: The volume of gas in your car�s gas tank depends on the number of miles you have driven.
Suppose you leave home with a full tank and begin driving at a constant speed. After driving 120 miles you have 12 gallons in your tank.
After driving 220 miles you have 8.66 gallons in your tank.
Assume the relationship is linear.

a. Find a function that models this situation. (Input miles driven and output gallons of gas in your tank.)

b. How many gallons does your gas tank hold when full?

c. How many miles can you drive before you will run out of gas?

d. What is your car's approximate fuel efficiency in miles per gallon?

Click here to see answer by josmiceli(19441)

Question 1104282: A sequence is defined recursively by the given formulas. Find the first five terms of the sequence.
an = 3a(n − 1) + 7 and a1 = 4
I thought it would be
a1=4
a2= 3(2-1)+7=10
a3= 3(3-1)+7=13
a4= 3(4-1)+7=16
a5= 3(5-1)+7=19
But those are wrong. What am I missing with this?
Click here to see answer by jim_thompson5910(35256)

Question 1104289: Find the nth term of a sequence who's first several terms are given
6/7 , 7/8 , 8/9, 9/10, ...

Click here to see answer by Alan3354(69443)

Question 1104279: show that (an)=(7-3n) is arithmetic and state the common difference and first 4 terms?
Click here to see answer by josgarithmetic(39617)

Question 1104307: Determine the common difference, the fifth term, the nth term, and the 100th term of the arithmetic sequence.
−t, −t + 4, −t + 8, −t + 12,
I have solved the common difference (4), the fifth term, -t+16, but I can't seem to figure out how to solve the nth term. I know once I have that, Ill be able to solve the 100th term, but I can't figure out that part
Click here to see answer by josgarithmetic(39617)

Question 1104296: Is the mean always the best measure of central tendency to use. True or false and why?
Click here to see answer by jim_thompson5910(35256)

Question 1104290: A sequence is defined recursively by the given forumlas. Find the first 5 terms.
an= (1)/(1+a(n-1) and a1=1
I am just not understanding recursive sequences.
Click here to see answer by ikleyn(52787)

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