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 375346: Give an equation for the sequence:
=1/2, -1/5, 1/10, -1/17, 1/26, -1/37

Click here to see answer by EdwinMcCravy(4)

Question 375995: How you guys find the sum of the integers from -4 to 23. Is what i did true? thank you.
S(28)= -28/2(-4+23)= -266.
Click here to see answer by jim_thompson5910(35256)

Question 375991: given 35/6, 47/8, 59/10, 71/12, 83/14,..., write an expression for the apparent nth term assuming n begins with 1. thanks
Click here to see answer by robertb(5830)

Question 376575: What does (i+1)(3-i)+(2i-1)=
Click here to see answer by Fombitz(32388)

Question 377318: Generate the general formula for the following sequence.
8, 13, 18, 23, 28, �
Click here to see answer by Fombitz(32388)

Question 377322: expand using the binomial theorem
Click here to see answer by robertb(5830)

Question 377461: In the sequence 16, 80, 48, 64, A, B, each term beyond the second term is the arithmetic mean (average) of the previous two terms. What is the value of D?
Click here to see answer by robertb(5830)

Question 377496: Write the series in sigma notation:
1 + 2 + 3 + ... + 99
2 3 4 100
Click here to see answer by ewatrrr(24785)

Question 377610: Please help me solve this equation:
Find the value of x and y, where x and y are real numbers
(x-y)+3i=7+yi
Click here to see answer by Fombitz(32388)

Question 378078: the general term of an infinite sequence is tn=K(0.3)^n-1 where kER
Click here to see answer by Fombitz(32388)

Question 378238: find the fifth term of the sequence,
a1 = 1/2, an = 2an-1
Click here to see answer by stanbon(75887)

Question 378345: Write a rule for the nth term of the arithmetic sequence that has the 2 given terms.
A(20)=240, A(15)=170
I understand how to write a rule for a sequence using the A(n)=A(1)+(n-1)d, but I do not understand how to get a rule without having the first term and common difference. Any help is really appreciated!
Thanks so much!
Click here to see answer by scott8148(6628)

Question 378496: Use inductive reasoning to name the next three numbers in the sequence: 17, 27, 42, 62, ...
answer= 87, 117, 152
Click here to see answer by IASFAIWLMHF(1)

Question 379497: For the sequence 1,5,9,13.... , give a formula for its nth term.
Click here to see answer by robertb(5830)

Question 379237: Write the first five terms of the arithmetic sequence. Find the common difference and the nth term of the sequence as a function of n.
a 1=2; a k+1=a k-4
I'm a very confused about this question. I understand the Fibonnaci sequence though. Do I solve this the same way?
Click here to see answer by richard1234(7193)

Question 379548: What is the next number in the following sequence? 25, 20, 16, 12 4/5.....
Multiply choices are:
a: 8 1/2
b: 6 2/5
c: 3 3/25
d: 10 6/25
Please show step by step how to solve this. Thank you
Click here to see answer by Alan3354(69443)

Question 379646: A rose garden has 21 bushes in one row, 17 bushes in the next row, then 13, and so on. If there are 66 bushes in the garden, in how many rows are they planted?

Click here to see answer by edjones(8007)

Question 379724: Find the nth term formula for the arithmetic sequence: 20,17,14,11
Click here to see answer by ewatrrr(24785)

Question 380157: Find the sum of the first n terms of the following arithmetic sequence.
a1 = 2, d = 2; n = 5.
Click here to see answer by rfadrogane(214)

Question 380239: for the sequence 1,4,7,10... find its n term
Click here to see answer by ewatrrr(24785)

Question 380245: For the sequence an=(4)/(n+1), its first term is _____, its second term is _____, its third term is _____, its fourth term is _____, its 100th term is _____
Click here to see answer by ewatrrr(24785)

Question 380243: For the sequence an=n+1, its first term is_____, second term is ____, third term is ____, fourth term is ____, its 100th term is ____
Click here to see answer by ewatrrr(24785)

Question 380241: Find the first five terms an=(4n!)/(n+3)
Click here to see answer by ewatrrr(24785)

Question 379877: In a certain sequence, each term is equal to
(3)
times the pervious term. If the fifth term in
the sequence is 27, what was the first term?
Click here to see answer by ewatrrr(24785)

Question 378767: in a geometric sequence the fourth term is 8 and the tenth term is 512. if common ratio is negative, find the first three terms.

Click here to see answer by ewatrrr(24785)

Question 376960: Find the 7th term of the geometric sequence −8, 4, −2, ...
(a) by listing out the first terms of the sequence.
(b) by using a formula for finding the nth term of a geometric sequence.
Then a second one which is similar is finding the 10th term of the g.s. 3, 6, 12, ...
(a) by listing out the first 10 terms of the sequence.
(b) by using a formula for finding the nth term of a geometric sequence.
Click here to see answer by ewatrrr(24785)

Question 376555: what is the and what is the algebraical expression for the sequence.
Click here to see answer by ewatrrr(24785)

Question 374462: Find a(1) for the arithmetic series with S(7) = 287 and d = 12. I know the answer is 5, but don't know the formula for solving the problem.
Click here to see answer by ewatrrr(24785)

Question 380275: How do i find the sum of the infinite geometric series: .996+(.996)squared+(.996)cubed + .....
Click here to see answer by Fombitz(32388)

Question 380464: The nth term is given,need help finding the first 4 terms, a8 and a12
an=(-1)n(2n+4)
Need help finding the indicated term of this sequence
an=7+150/n;a17
How do I prove that for every natural number n,
1+3+5...+(2n-1)=n2
How do I find the sum, if it exist
10+1+1/10+1/100...
How do I find the sum of the first 14 terms of the geometric series
20-25+25/2...
How do I find the indicated term
4,8,16,32 and the 17th term
Click here to see answer by solver91311(24713)

Question 380255: y(x+y3)

Click here to see answer by Fombitz(32388)

Question 380584: 1. Show that the sum of any two odd numbers is always an even number.
2. Show that the product of any two even numbers is divisible by four.
Click here to see answer by ewatrrr(24785)

Question 380955: find a number whose product with 9 is the same as it sum with 56
Click here to see answer by mananth(16946)

Question 381489: What is the gerneral term (in sigma notation) of this Fourier series:
-Pi/2 <= x < pi/2 x=pi
pi/2 <= x < pi x=2pi-2x
-pi<= x < =pi/2 x=2pi+2x

Click here to see answer by stanbon(75887)

Question 382110: what is the sum of terms if the first 8 terms are :15,19,23,27,31,35,39,43
Click here to see answer by user_dude2008(1862)

Question 382111: what is the sum of terms if the first 12 terms are :2.6,3.1,3.6,4.1,4.6,5.1,5,6,6.1,6.6,7.1,7.6,8.1

Click here to see answer by user_dude2008(1862)

Question 382298: What is the general formula for the following series.
5,9,18,34,59,95
Click here to see answer by stanbon(75887)

Question 382298: What is the general formula for the following series.
5,9,18,34,59,95
Click here to see answer by Edwin McCravy(20056)

Question 382537: The sum of two numbers is 135. The difference between them is 9. Find the numbers.
Click here to see answer by nerdybill(7384)

Question 382729: The sum of two numbers is 201 and the difference between them is 11. Find the two numbers.
Click here to see answer by richard1234(7193)

Question 383992: What are the next two numbers in the sequence: 1/32, 4/16, 9/8, 16/4?
Click here to see answer by richard1234(7193)

Question 384044: EVALUATE 9C6
Click here to see answer by robertb(5830)

Question 384043: GIVEN THAT P(A)=0.3 AND P(B)=0.5, AND P(A AND B)=0.12, DETERMINE P(A|B)
Click here to see answer by robertb(5830)

Question 384236: Question: There are 9 horses in a race. In how many ways can the first 3 positions of the order of the finish occur. Assuming no ties.
I did the 9*8*7*6.... method but not sure what next. I tried dividing by 6 but a mistake.
Click here to see answer by Alan3354(69443)

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