Questions on Algebra: Sequences of numbers, series and how to sum them answered by real tutors!

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Question 1096580: Geometric Series Question:
a, a-12, a+12 are the first three terms of a geometric sequence
1) What is the value of a?
2) Calculate the sum for the first 10 terms
Click here to see answer by ikleyn(52788)

Question 1096579: Geometric Series Question:
a, a-12, a+12 are the first three terms of a geometric sequence.
1) What is the value of a?
2) Calculate the sum of the first 10 terms.
Thank you
Click here to see answer by ikleyn(52788)

Question 1096591: Use mathematical induction to prove 6 is a factor of n^3 + 3n^2 + 2n. Please pls pls pls help me. Thankyou.
Click here to see answer by ikleyn(52788)

Question 1096592: Use mathematical induction to prove 3 is a factor of 4^n - 1. I'm realky confused. Please help me. Thank you so much.
Click here to see answer by greenestamps(13200)

Question 1096566: if the fifth term of arithmetic sequence is 23 and the sum of the first ten terms of the sequence is 240 then wich of the following is the sum of the first sixty terms of this sequence?
A.2489
B.4440
C.1640
D.1980
Click here to see answer by ikleyn(52788)

Question 1096567: 2.the sum of integers from 1 to 100 wich are not divisible by 3 or 5 is
A.2489
B.4735
C.2317
D.2632
Click here to see answer by greenestamps(13200)

Question 1096728: The current value of a vehicle is ksh.128,000.If this vehicle has been depreciating by a fifth of its value every year, find its value 4 years ago.
Click here to see answer by Boreal(15235)

Question 1096239: 288 286 295 267 332 ?
Click here to see answer by Edwin McCravy(20056)

Question 1094570: If the arithmetic mean of two numbers a & b (0
Click here to see answer by Edwin McCravy(20056)

Question 1096825: Three consecutive terms of a geometric sequence are x - 3, 6 and x + 2.
Find the possible values of x.
Click here to see answer by Boreal(15235)

Question 1096834: the first and last teem of an AP are 0 and 108.if the sum the series is 702.find d number of term in the AP and the common difference
Click here to see answer by Boreal(15235)

Question 1096827: Ramiro walks to work each morning. During the first minute he walks 80 metres. In each subsequent he walks 90% of the distance walked during the previous minute.
The distance between his house and work is 660 metres. Ramiro leaves his house at 08:00 and has to be at work by 08:15. Explain why he will not be at work on time.
Click here to see answer by Boreal(15235)

Question 1096823: 1a. Consider the following sequence of figures.
Figure 1 contains 5 line segments.
Figure 2 contains 9 and figure three contains 13.
Given that figure n contains 801 line segments, show that n=200.
Click here to see answer by Edwin McCravy(20056)

Question 1096859: Determine if the sequece is arithmetic. If the sequence is arithmetic, find the common difference.
a_n = n(n+9)
Click here to see answer by jim_thompson5910(35256)

Question 1096858: Rewrite the series using summation notation. Use 1 as the lower limit of summation.
3+(-9)+27+(-81)+.....+(-6561)
Click here to see answer by Boreal(15235)

Question 1094569: If 25/k = 1^2 -2^2/5 + 3^2/5^2 - 4^2/5^3+.......infinity ,
then what is the value of k?
Click here to see answer by Edwin McCravy(20056)

Question 1096913: find d seventh term of d following.
Click here to see answer by richwmiller(17219)

Question 1096826: 3a. The first three terms of an arithmetic sequence are u1 = 0.3, u2 = 1.5, u3 = 2.7.
Find the common difference.
3b. Find the 30th term of the sequence.
3c. Find the sum of the first 30 terms.
Click here to see answer by ikleyn(52788)

Question 1096965: Mary has accepted a teaching job that pays $25,000 for the first year. According to the Teacher's Union, Mary will get guaranteed salary increases of 3% per year. If Mary plans to teach for 27 years, what will be her total salary earnings?
Click here to see answer by Boreal(15235)

Question 1097029: An arithmetic sequence is given by 5, 8, 11, ....
Write down the value of d.
Find
I. u100
II. S100
Given that un = 1502, find the value of n.
Click here to see answer by stanbon(75887)

Question 1097076: A middle school mathematics teacher accepts a teaching position that pays $30,000 per year. Each year, the expected raise is $ 1,000. How much total money will this teacher earn teaching middle school mathematics over the first 30 years?
Click here to see answer by jorel1380(3719)

Question 1097127: Find next number 8,8,0,2,8,?
Click here to see answer by ikleyn(52788)

Question 1097126: Find next number 2, 7, 0, 3, 6
Click here to see answer by ikleyn(52788)

Question 1097195: Consider the following sequence of figures.
Figure 1 contains 5 line segments.
Figure 2 contains 9 and figure three contains 13.
Given that figure n contains 801 line segments, show that n=200. already did this first part. I need to figure out how to do the part below
Find the total number of line segments in the first 200 figures.

Click here to see answer by ikleyn(52788)

Question 1097187: A G.p has 8terms.its first and last terms are 0.3 and 38.4.calculate
commom ratio
Click here to see answer by ikleyn(52788)

Question 1097185: A G.p has 8terms.its first and last terms are 0.3 and 38.4.calculate
commom ratio
Click here to see answer by Boreal(15235)

Question 1097200: I ONLY NEED TO KNOW PART C
5a. The sides of a square are 16 cm in length. The midpoints of the sides of this square are joined to form a new square and four triangles. The process is repeated twice.
Let Xn denote the length of one of the equal sides of each new triangle.
Let An denote the area of each new triangle.
The following table gives the values of Xn and An, for 1 less than or equal to n less than or equal to 3.
N 1 2 3
Xn 8 __ 4
An 32 16 __
(First blank I got 6, second blank I got 8)
5b. The process described above is repeated. Find A6.
A6 = 8
5c. Consider an initial square of side length k cm. The process describes above is repeated indefinitely. The total area of the shaded regions is k cm^2. Find the value of k.
Click here to see answer by greenestamps(13200)

Question 1097251: solve this.
3 7 14 27 52 ......
Click here to see answer by greenestamps(13200)

Question 1097251: solve this.
3 7 14 27 52 ......
Click here to see answer by Edwin McCravy(20056)

Question 1097196: 5a. The sides of a square are 16 cm in length. The midpoints of the sides of this square are joined to form a new square and four triangles. The process is repeated twice.
Let Xn denote the length of one of the equal sides of each new triangle.
Let An denote the area of each new triangle.
The following table gives the values of Xn and An, for 1 less than or equal to n less than or equal to 3.
N 1 2 3
Xn 8 __ 4
An 32 16 __

5b. The process described above is repeated. Find A6.

5c. Consider an initial square of side length k cm. The process describes above is repeated indefinitely. The total area of the shaded regions is k cm^2. Find the value of k.
Click here to see answer by greenestamps(13200)

Question 1097243: f(1) = 4, d = 3
Click here to see answer by Alan3354(69443)

Question 1097514: Please help me solve this equation
The question is Insert three Geometric Mean between 4 and 5
Click here to see answer by Alan3354(69443)

Question 1097513: Please help me to solve this equation
The question is Insert four geometric mean between 243 and 1.

Click here to see answer by Alan3354(69443)

Question 1097537: 75 ? 124 ? 189
Click here to see answer by Alan3354(69443)

Question 1097539: Given a geometric sequence where t3=17 and t6=136, t7 would be
Click here to see answer by ikleyn(52788)

Question 1097575: Write the following geometric series in summation notation
-9/2 + 3/2 - 1/2. + 1/6 - ...+. 1/39366
Using the formula for the sum of a geometric series, compute the sum.
Click here to see answer by KMST(5328)

Question 1097622: The 28th term of an AP is - 5.find it's common difference if it's first term is 31

Click here to see answer by Jeetbhatt10th(11)

Question 1097768: the sum of 7 and 2 added to 4 times a number
Click here to see answer by ikleyn(52788)

Question 1097929: What is the numeric pattern for -6;-4;-2;....
Click here to see answer by Fombitz(32388)

Question 1097970: What is the 27th term of 19, 39, 59, 79...

Click here to see answer by ikleyn(52788)

Question 1097954: State the rule . Then write the next two terms. 800, 400, 200,
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