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 825245: Hi! I'm stuck on this question
∞
Σ (-1)x
1
It's sigma sign with infinity sign on the top, 1 on the bottom and (-1) to the power of x on the side. I have no idea how to work it out so your help would be greatly appreciated. Thank you!
Click here to see answer by tommyt3rd(5050)

Question 830326: A girl is the eldest of 15 children and each child is exactly a year and a half apart. The eldest is eight times the youngest age. What is the oldest age?
Click here to see answer by Edwin McCravy(20056)

Question 830390: A sequence has a third term of 18, and a common ratio of 3.
What is the fifth term?

Click here to see answer by tommyt3rd(5050)

Question 826541: Find the sum: (-2)+0+2+...+76.
Show all steps.
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Question 830500: If the 10th term of a geometric sequence is 243 times larger than the 5th term, what is the common ratio of the sequence?
Click here to see answer by reviewermath(1029)

Question 830581: On a road map where 1 inch = 60 miles, you measure a distance of 19.65 inches from the starting point to destination. How many miles in actual distance is it from the start to the destination?
Click here to see answer by JulietG(1812)

Question 830585: You have just won the lottery and burying most of your lump sum in your back yard. The spot where you buried your treasure is 432 feet from your back door. If you made a map where 1 inch = 75 feet, how many inches on the map would represent the 432 feet actual distance?
Click here to see answer by JulietG(1812)

Question 830646: state three consecutive terms in the arithmetic progression 40,33,26 ...which sum up to 15
Click here to see answer by reviewermath(1029)

Question 830650: Skyler is a baseball player who trains everyday . He runs 1 3/8 miles everyday. How many miles does he run in32 days
Click here to see answer by JulietG(1812)

Question 826461: 1) Suppose Tn= a+(n-1)d is an AP with first term "a" and difference "d". Show that the sequence Un=2^(Tn) is a GP and find its first term and ratio.
Thanks!!

Click here to see answer by tommyt3rd(5050)

Question 827602:
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Question 827009: Given 50+42+34+26+18+ ... find n such that Sn=182
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Question 830780: Hi there, someone helped me earlier this week and it was awesome! Thank you!
Here's my question...
It's about Arithmetic Sequences and finding the nth term.
Chem deposited $115 into a savings account. Each week thereafter, he deposits $35 into the account.
A. Write the formula to find the total amount Chem has deposited for n weeks after his initial deposit.
B.How much had Chem deposited 30 weeks after his initial deposit?
I am using the formula: a_n = a_1 + (n-1)d
a_1=115
d=35
I got 35n + 80; $1,130
BUT...the book answer says 35n + 115; $1,165
I am wondering if I'm reading the problem wrong and the key is how much he deposited "after" the initial deposit. Thanks so much for answering my question!
Isabella
Click here to see answer by richwmiller(17219)

Question 830143: 2/3w+9=13 w=?
Click here to see answer by Fombitz(32388)

Question 830824: 7, 21, 8, 72, 9, ?
Click here to see answer by JulietG(1812)

Question 830823: 2, 7, 26, 101, 400, ?
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Question 830793: The first term of sequnce is x. To get the next term multiply the previous term by 2 and add 1.the third term of the sequence is 21.find the value of x. Plzz help me find the answer...its 4.5 in the book gcse
Click here to see answer by JulietG(1812)

Question 830902: The 11th term of an arithmetic sequence is 57 and the sum of the first and the fourth terms is 29.Determine the first 3 terms of the sequence. . .please help me step by step
Click here to see answer by Edwin McCravy(20056)

Question 830892: the 3rd and 6th term of a geometric progression are 48 and 14 2/9 respectively. Write down the 1st 4 terms of the geometric progression.
Click here to see answer by Edwin McCravy(20056)

Question 830929: I would like to know how to determine the general term of the following number pattern:
7; 24; 51; 88
Click here to see answer by richwmiller(17219)

Question 831181: 10*7+10*(-5) please help solve

Click here to see answer by oscargut(2103)

Question 831185:

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Question 831211: given the arithmetic sequence 58, 73, 88 determine:
-the general term, tn
-the value of the tenth term, t10
-the sum of the first ten terms, S10
Click here to see answer by Elomeht(22)

Question 831389: What comes next in this
series?
5, 7, 6, 8, 7, ?
Click here to see answer by Fombitz(32388)

Question 831708: The 11th term of an arthmetric sequence is 57 and the sum of the first and fourth terms is 29. Determine the first 3 terms of the sequence

Click here to see answer by hovuquocan1997(83)

Question 831867: Look at the number series below.
16, ( ? ), 13, 15, 6, 24
If the average of the series is 15, then what is the missing number?

Click here to see answer by Fombitz(32388)

Question 832211: Find the 20th term from the last term of AP: 3,8,13...253
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Question 832337: 3/5*10/3+1/2*12

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Question 832467: Solve the following system of three equations in three variables:
400a + 20b + c = 25
1600a + 40b + c = 105
3600a + 60b + c = 305
a=
b=
c=
Click here to see answer by richwmiller(17219)

Question 833151: What two numbers is the sum of 20 and when the second number is subtracted by the first number, the difference is 14?
Click here to see answer by rm29924(97)

Question 833146: what is Y, if a =10, b=.75 and C=100
I cannot figure the formula to solve this.
can You help?
I know the answer is 120, but I cannot figure the formula to resolve this.
Click here to see answer by Fombitz(32388)

Question 833287: Let Pn denote the population size of ring-necked pheasants on Protection
Island on 1 April, n years after 1937; thus P0 represents the population
size on 1 April 1937, which is 8. Assume that the number of births in each
subsequent year (from 1 April to 31 March) is 2.6Pn (that is, 260% of Pn),
and the number of deaths in each subsequent year is 0.4Pn (40% of Pn).
During the (n+ 1)th year, the �joiners� will be the pheasants born
during the year, of which there are 2.6Pn, and the �leavers� will be the
pheasants that die, of which there are 0.4Pn. The diﬀerence between
births and deaths gives the increase in the population size during the
year (since we are assuming that there is no migration), so
Pn+1 − Pn = 2.6Pn − 0.4Pn
= 2.2Pn.
Thus the sequence Pn is given by
P0 = 8, Pn+1 = 3.2Pn (n = 0,1,2,...).
[I NEED TO UNDERSTAND WHERE 3.2 APPEARS FROM]

Click here to see answer by stanbon(75887)

Question 833412: PLEASE HELP! I don't know how I would solve this : An arithmetic sequence is defined: k, 15, k+18 what is the value of k? PLS ANSWER THANKS
Click here to see answer by josgarithmetic(39617)

Question 833482: Please help me with this sequence problem
Look at this sequence:7,12,17,22
What will the next three numbers be in the sequence? 27,32,37
Will 200 be in the sequence and how do you know?
Click here to see answer by Edwin McCravy(20056)

Question 833991: find a number whose product with seven is the same as its sum with twenty four
Click here to see answer by stanbon(75887)

Question 734533: 7^(1/4) x 49^(-5/8)

Click here to see answer by lambo(6)

Question 834464: find the missing term of number series 3,10,20,33,49,68, ?
Click here to see answer by KMST(5328)

Question 834584: What is the value of the expression 7 �25 � 3 � 48?
Click here to see answer by stanbon(75887)

Question 834700: Twenty-four is less than or equal to the sum of 35 and x
Click here to see answer by jim_thompson5910(35256)

Question 834803: What is the missing term, a, in the pattern below?

20, 10, a, 2.5, 1.25

Click here to see answer by Alan3354(69443)

Question 834848: Solve: 3n - 16 = or < 8n + 29

Click here to see answer by Fombitz(32388)

Question 834538: What Are The Next Three Terms In 6,7,13,20,33
What Is The 17th term in 2,6,18,54
What is the 50th term in 2,9,16,23
Click here to see answer by Edwin McCravy(20056)

Question 835036: Find S[5] for the arithmetic sequence with
a[3]=39 and a[5] =61
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