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 274055: what is the next number in the following pattern 1, 1/2, 1/4, 1/8
A. 1/10
B. 1/12
C. 1/14
D. 1/16
Click here to see answer by asuar010(338)

Question 274050: Consider the series: 3, 4, 6, 9, 13, _____ what comes next?
A. 15
B. 16
C. 17
D. 18
Click here to see answer by asuar010(338)

Question 274048: consider the series :27, 24, 20, 15, 9, 2, what come next ?
Click here to see answer by Kaley2(4)

Question 274609: Given that
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25
Determine a pattern and use it to find the sum of the first 300 odd numbers
Click here to see answer by Alan3354(69443)

Question 274609: Given that
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25
Determine a pattern and use it to find the sum of the first 300 odd numbers
Click here to see answer by CharlesG2(834)

Question 274700: Find the missing term in the arithmetic sequence: ...,2,___,14,...
Click here to see answer by edjones(8007)

Question 274937: Mary can paint a house in 4 hrs.John can paint the same house in 6 hrs. How long will it take to paint house together. First I converted hours to minutes, added them together, then divided by two. please help me set up this problem correctly.
Click here to see answer by Alan3354(69443)

Question 275226: Determine a formula for the arithmetic sequence that begins 1.1, 3.3, 5.5. What is the 10th term of this sequence?
I literally added the 2.2 until I got to the 10th term which is 20.9, but I have no idea on how to construct a real formula. Any help would be greatly appreciated.(:
Click here to see answer by user_dude2008(1862)

Question 275322: A display of cans on a grocery shelf consists of 20 cans on the bottom, 18 cans in the next row, and so on in an arithmetic sequence, until the top row has 4 cans. How many cans, in total, are in the display?
please use the equation needed so i know how to do it.
thank you:)
Click here to see answer by stanbon(75887)

Question 275349: List the first six terms of the sequence defined recursively by
z0 = 0
z1 = 1
z2 = 2
What exactly, does this imply, and how would I start it? I'm so confused.
Click here to see answer by jim_thompson5910(35256)

Question 275375: what is the sum of the integers between 20 and 480 that are multiples of 11?
please use the equation needed, thank you:)
Click here to see answer by user_dude2008(1862)

Question 275375: what is the sum of the integers between 20 and 480 that are multiples of 11?
please use the equation needed, thank you:)
Click here to see answer by Edwin McCravy(20056)

Question 272585: write the following sums using summation notation

1+6+13+22+33
Click here to see answer by wmclardy(1)

Question 276177: How do I solve this word problem:
Two consecutive positive odd numbers have the property that their product plus the square of their difference equals 147. Find the larger of these two numbers.
Click here to see answer by ankor@dixie-net.com(22740)

Question 276237: the diffrence of what integer and 5 is eqaul to 32
Click here to see answer by solver91311(24713)

Question 276098: An arithmetic sequence has initial term 6 and common difference 624. A geometric sequence has initial term 2 and common ratio 3. Determine an n so the nth term of the arithmetic sequence is that same as the nth term of the geometric sequence.
I'm not sure how this works, and the only hint I was given was that initial term = a0. Any help would be so great, thanks for your time. (:
Click here to see answer by scott8148(6628)

Question 276505: In this sequence below, each term after the first term is 1/4 of the term preceding it. What is the 6th term of this sequence?
320, 80, 20, ...
Click here to see answer by checkley77(12844)

Question 276501: What is the greatest of five consecutive integers if the sum of the integers equals 135?
Click here to see answer by checkley77(12844)

Question 276507: The perimeter of a triangle is 15. The lengths of the sides are integers. If the length of one side is 6, what is the shortest possible length of another side of the triangle?
Click here to see answer by Edwin McCravy(20056)

Question 276506: If the average (arithmetic mean)of three different positive integers is 60, what is the greatest possible value of one of the integers?
Click here to see answer by Fombitz(32388)

Question 274056: what is the next number in the following pattern 1, 1/2, 1/4, 1/8
A. 1/10
B. 1/12
C. 1/14
D. 1/16
Click here to see answer by sunshine _ 1(1)

Question 277627: ... 23, 25, 27, 29... which expression describes the sequence?
A. 3x - 3
B. 3 + 2x
C. 2x - 2
D. x squared + 1
Click here to see answer by nabla(475)

Question 278195: Find the sum of the first terms of arithmetic sequence 21,16,11,6
Click here to see answer by jim_thompson5910(35256)

Question 278866: what number best completes the series below?
140,70,35,17.5.....
Click here to see answer by richwmiller(17219)

Question 271629: Is 0 even or odd???Explain...
Click here to see answer by Inkyvoyd(17)

Question 279700: P = (1 - 1/2)(1 - 1/3)(1 - 1/4)...(1 - 1/16)
The three dots in the product above represent eleven missing factors of the form (1 - 1/n), where n represents all of the consecutive integers from 5 to 15, inclusive. What is P equal to?
a. 1/16
b. 1/2
c. 7/8
d. 15/16
Click here to see answer by CharlesG2(834)

Question 280961: 2, 3, 5, 5, 3, 2, ...
The first three terms of the sequence are 2, 3, and 5. After that, subsequent terms are produced by switching the order of the previous three numbers. What is the sum of the squares of the 14th and 43rd terms?
Click here to see answer by stanbon(75887)

Question 280913: 2c^2*2c^4=
Click here to see answer by checkley77(12844)

Question 281707: how do you find the 10th term of (x+y)^20?
Click here to see answer by stanbon(75887)

Question 282814: Choose the explicit formula for the sequence 1, 1/4, 1/9, 1/16, ... Then find a15.
(15 is below a. Not sure how to type that here, so I posted a pic of the question and answers here: http://i44.tinypic.com/16lwyzn.jpg)
Click here to see answer by Alan3354(69443)

Question 282815: A recursive formula for a sequence is an=an-1 +2n where a1=1. Write the first five terms of the sequence.
(N, n-1, and 1 are all below the a. Wasn't sure how to type the whole question, pic here: http://i39.tinypic.com/2cedxl.jpg)
Click here to see answer by Edwin McCravy(20056)

Question 282813: Choose the recursive formula for the sequence 7, �1, �9, �17, ... Then choose the next term.
a. an= an - 1 � 7, where a1= 7; �24
b. an= an - 1 � 8, where a1= 7; �25
c. an= an - 1 � 7, where a1= �17; �25
d. an= an - 1 + 8, where a1= 7; �25
(n, n-1, and 1 are below the a but not sure how to write that here. I posted a pic here: http://i39.tinypic.com/33c0ocl.jpg)
Click here to see answer by Alan3354(69443)

Question 283474: Find two numbers whose sum is 55 and product is 600.
Click here to see answer by oberobic(2304)

Question 283867: In June, you start a holiday savings account with a deposit of $50. You increase each monthly deposit by $2 until the end of the year. How much money will you have saved by December? 62
Click here to see answer by ngonzalez(1)

Question 283866: Explain how the common ratio for a geometric sequence with positive terms determines whether the terms increase or decrease.
Click here to see answer by jim_thompson5910(35256)

Question 284080: Find the indicated term of each arithmetic sequence:
42nd term: a1 = 10; d = 6
I need help with solving this problem.
Thanks
Click here to see answer by checkley77(12844)

Question 285438: find the first four terms of a sequence for 2n+4 divided by 2
Click here to see answer by user_dude2008(1862)

Question 285530: What term fits in the blank space in the sequence 1/2, 4, 1/8, 16,__ ,64, � � � ?
a 1/24 b 1/32 c 1/40 d 1/42 e none of these
Click here to see answer by checkley77(12844)

Question 285501: series of 13, 18, 16, 21, 19
Click here to see answer by checkley77(12844)

Question 285623: What is the sum equation for this promblem : 1-(1/2)+(1/4)-(1/8)+...-(1/128)
Click here to see answer by richwmiller(17219)

Question 285528: In numbering the pages of a book, a total of 510 digits were printed. If the first page is numbered 1, how many pages does the book have?
(A)170 (B) 199 (C) 200 (D) 206 (E) 198

Click here to see answer by Alan3354(69443)

Question 286007: Find the 15th term and the sum of the first 15 terms for the following sequences.
a) 12, 17, 22, �.
b) 4, 10, 16, �.
Click here to see answer by nerdybill(7384)

Question 286334: What is the next term in the sequence and what would be the rule in the nth term.. PROBLEM:1,10,100,1000
Click here to see answer by richwmiller(17219)

Question 286343: Find three numbers in geometric progression whose sum is 21 and sum of their squares is 189?
Click here to see answer by texttutoring(324)

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