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 877542: Can someone help me with this problem?
A ball is dropped from 180 cm above the floor.which each bounce,it rebounds to 65% of its previous height.
Use a calculator to find the first ten heights,with the initial drop height being the first of the sequence.then find the first ten partial sums of this sequence of heights:s1,s2,s3,s4
Thank you
Click here to see answer by Alan3354(69443)

Question 877695: What is the formula for:
1+(1+2)+(1+2+3+4)+(1+2+3+4+5+6+7+8)+...
and how is it derived? I do know the formula btw (-: but I am not sure how to derive it.
Click here to see answer by richard1234(7193)

Question 877661: find the sixth term of the geometric sequence 2,6,12,20,30,..
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Question 877622: For the arithmetic sequence with a1=3 and a20=117, find the common difference D.
Click here to see answer by Theo(13342)

Question 877937: Write a recursive formula for each sequence:
a. 8,14,20...
b. 9,3,1,1/3...
c. 3, -6,12,-24
Click here to see answer by richard1234(7193)

Question 877985: What should come in place of question mark in the following series-
1,3,9,21,81,?,729
Ans-
1. 243
2. 324
3. 686
4. 162
Click here to see answer by Fombitz(32388)

Question 878095: How do you determine the missing sides so that the measurements will produce a right angle
300:b :500
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Question 878328: Show that the sum of any three consecutive numbers is a multiple of 3.
Show that the sum of any four consecutive numbers is always even.
Click here to see answer by Alan3354(69443)

Question 878423: The tenth term of an arithmetic sequence is 20 and the fifth term is 0. Find the sum of the terms from the eighth to the eighteenth, inclusive.
Please help! Thank you!
Click here to see answer by Fombitz(32388)

Question 877525: Which Sequence is geometric and has 1/4 as it's fifth term and 1/2 as the common ratio?
1, 1/2, 1/4, 1/8
0r
1/4, 1/2, 1, 2
or; 1/72, 1/36, 1/18, 1/9 or
8, 4, 2, 1
Click here to see answer by Fombitz(32388)

Question 878604: 14,a,b,c,d,81 what is the sum of a+d?
Click here to see answer by richwmiller(17219)

Question 878349: Find the number of terms and the values of the arithmetic means that should be inserted between 1 and 50 in order to make the sum of the seris equal 459.
Click here to see answer by richwmiller(17219)

Question 878672: if a.m and g.m for two numbers are 6.5 and 6 then two numbers are
Click here to see answer by jim_thompson5910(35256)

Question 878673: in g.p product of first three term is 729/8 middle term is
Click here to see answer by josgarithmetic(39618)

Question 878901: If 5, x, y, z, 405 are the first term of a GP , find the value of x, y, z.
Click here to see answer by KMST(5328)

Question 878931: the sum of three of a g.p. is 21 and the sum of their squares is 189. find the numbers.
Click here to see answer by dkppathak(439)

Question 879040: Two arithmetic mean between -6 and 14 is
Click here to see answer by MathLover1(20850)

Question 879030: I am trying to find the sum of the following sequence:32+33+34+35+...+113. I can do any when it starts with 1, but I cannot grasp how to solve this one.
Thank you
Click here to see answer by josgarithmetic(39618)

Question 879052: 720,?,120,30,6,1
Click here to see answer by AnlytcPhil(1806)

Question 878997: The least value of n for which sum of n terms of series 1+3+9(3square)+.....is greater than 7000 is

Click here to see answer by AnlytcPhil(1806)

Question 879093: What is 400 miles divided into three months?

Click here to see answer by JulietG(1812)

Question 879130: What is the next number in series 1 4 11 24 47 88 163
Click here to see answer by richwmiller(17219)

Question 879193: 2+2/3+2/9+2/27+...
Click here to see answer by ewatrrr(24785)

Question 879191: 2+2/3+2/9+2/27+...
Click here to see answer by ewatrrr(24785)

Question 879649: Here is a series written in expanded form:
3 + 8 + 13 + ... + 28
Which of the following summation notations represents this series?

Click here to see answer by richard1234(7193)

Question 879621: write the series -5+5+15+25+35 using summation notation
Click here to see answer by josgarithmetic(39618)

Question 879729: The third and fourth terms of a sequence are 101 and 83. If the first differences are a constant, find the first 5 terms in the sequence?

Click here to see answer by ewatrrr(24785)

Question 879779: is this a geometric sequence.
1, -2, 4, -8, 16 true or false
is this a geometric sequence
2, 4, 8.5, 16 true or false

Click here to see answer by ewatrrr(24785)

Question 879622: write a rule for the nth term of the arithmetic sequence 2,9,16,23,30...What is a^16?
Click here to see answer by richwmiller(17219)

Question 879999: write the nth rule, given 256,64,16,4
Click here to see answer by Fombitz(32388)

Question 880176: tell whether the sequence 3, -9, 27, -81 is geometric
Click here to see answer by josgarithmetic(39618)

Question 880183: what will be the next number in the series 1,4,20,168,?

Click here to see answer by Edwin McCravy(20056)

Question 880182: 1,4,20,126,?
Click here to see answer by Edwin McCravy(20056)

Question 880060: Find the 45th partial sum of the geometric sequence
8+12+18+27+....
Click here to see answer by Edwin McCravy(20056)

Question 880216: (sigma i = 1 to 2014 i^2 ) / (sigma i = 1 to 2014 i ) ?
Click here to see answer by Edwin McCravy(20056)

Question 880265: Find the sum of the first 40 terms of 14,17,20,...

Click here to see answer by richwmiller(17219)

Question 880063: Find the number of terms in the sequence: -6,-2,2,6,.......70
Click here to see answer by richwmiller(17219)

Question 880181: If in coded language naval=3646,manish=248912,Vijay=49433.then suresh=?
Click here to see answer by richwmiller(17219)

Question 880040: The first term of a geometric sequence is 25, and the forth term is 1/5. Find the common ratio and the fifth term.
Click here to see answer by richwmiller(17219)

Question 880066: In a geometric sequence, a3=9, a6=9/8, find a 12
Click here to see answer by richwmiller(17219)

Question 880057: Determine the seating capacity of an auditorium with 18 rows of seats if there are 20 seats in the first row, 24 seats in the second row, and 28 seats in the third row and so on
Click here to see answer by richwmiller(17219)

Question 879703: 3 14 39 84 115 what will be the next number

Click here to see answer by richwmiller(17219)

Question 879195: The next number in the series 1 4 11 24 47 88 163 is 304.what is the logic used in solving this?
Click here to see answer by richwmiller(17219)

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