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 1187213: The sum of four numbers in an arithmetic progression is 98. The sum of their squares is 3006. Find the third number.
Click here to see answer by ikleyn(52787)

Question 1187260: It is a kind of sequence where every term after the first is obtained by multiplying a constant called common ratio. *
1 point
Harmonic Sequence
Fibonacci Sequence
Geometric Sequence
Arithmetic Sequence
Click here to see answer by ikleyn(52787)

Question 1187317: Please help me find the 50th term in the arithmetic sequence.
5,9,13,17,...... Also, please explain it to me, thank you!
Click here to see answer by josgarithmetic(39617)

Question 1187317: Please help me find the 50th term in the arithmetic sequence.
5,9,13,17,...... Also, please explain it to me, thank you!
Click here to see answer by greenestamps(13200)

Question 1187380: If the 2nd and 5th term of a geometric progression are -6 48 respectively, find the sum of the 5th first four terms

Click here to see answer by Boreal(15235)

Question 1187380: If the 2nd and 5th term of a geometric progression are -6 48 respectively, find the sum of the 5th first four terms

Click here to see answer by ikleyn(52787)

Question 1187548: 76, 80, 88, 95, 100, 101
Click here to see answer by greenestamps(13200)

Question 1187638: T3=24 T6=60
FIND THE COMMON DIFF AND THE FIRST TERM (a)
Click here to see answer by Theo(13342)

Question 1187650: The seventh term of an arithmetic sequence is 25. Its first, third, and 21st
term form a geometric sequence. Find the first term and the common
difference of the sequence
Click here to see answer by greenestamps(13200)

Question 1187888: the 17 th term of sequence 3, 9, 27, 81, and so on.
Click here to see answer by ikleyn(52787)

Question 1187892: What is the pattern for this sequence: 16, 8, 9, 12, 9, 16, 16, 9, 14
Click here to see answer by greenestamps(13200)

Question 1188018: Given that the first term and the common ratio of a geometric sequence are 3/8 and -2 respectively, and the sum of the first n terms is -8,191.875, find the sum of the (n+1) term to the (n+5) term.
Click here to see answer by greenestamps(13200)

Question 1188231: Express the nonterminating repeating decimal 2.045045045... as a fraction.
Click here to see answer by Edwin McCravy(20056)

Question 1188231: Express the nonterminating repeating decimal 2.045045045... as a fraction.
Click here to see answer by mccravyedwin(407)

Question 1188230: Find the sum of the infinite geometric series 1, 0.5, 0.25, ...
Click here to see answer by math_helper(2461)

Question 1188228: How many numbers between 5 and 200 are divisible by 3?
Insert four arithmetic means between -1 and 14
Click here to see answer by Edwin McCravy(20056)

Question 1188229: A ball dropped from a height of 100 m and after each fall, it rebounds 1/3 of the
distance from which it fell. Find the total distance travelled by the ball before
coming to rest.
I honestly cannot figure out how to write the working equation for it. Please help, thank you!
Click here to see answer by MathLover1(20850)

Question 1188227: Are these sequences arithmetic, geometric, or neither?
(1) 3, 5, 8, ...
(2) 2a, 4a^2, 8a^3, ...
I think the first is neither and the second is geometric but need guidance, thank you so much!
Click here to see answer by MathLover1(20850)

Question 1188246: A pyramid of blocks has 26 blocks at the bottom row and 2 fewer blocks each
successive row thereafter. How many blocks are there in the pyramid?
Click here to see answer by Boreal(15235)

Question 1188248: Find the 20th term of a geometric sequence whose third term is 1 and common
ratio is -3.
I tried doing
a₂₀= 1 (-3) ²⁰ ⁻ ³
a₂₀= (-3)¹⁷
The answer I got was -129140163 but it doesn't feel correct. I think my equation is wrong but I don't know how else to put it.
Click here to see answer by Boreal(15235)

Question 1188249: Find the 10th term of a geometric sequence whose 5th term is 81 and whose
ninth term is 16.
I solved it as
16 = 81r⁵⁻¹
16 = 81r⁴
r = -2/3, 2/3
I used the positive value and did
a₁₀= 81(2/3)⁶⁻¹
a₁₀= 32/3
Is this correct? Thank you
Click here to see answer by Boreal(15235)

Question 1188296:
Click here to see answer by ikleyn(52787)

Question 1188392: In the sequence 456, 471, 483, 498, ... each term is equal to the previous term added to the sum of its digits. A number NOT in the sequence is
a) 1869 b) 1950 c) 3477 d) 4569 e) 5789
Click here to see answer by ikleyn(52787)

Question 1188394: In the sequence 457, 473, 487, 506, ... each term is equal to the previous term
added to the sum of its digits. A number NOT in the sequence is
a) 1864 b) 1949 c) 3466 d) 4569 e) 5767

Click here to see answer by ikleyn(52787)

Question 1188438: The sum of n term of a series is n^2+2n for all value of n.find the first three terms of the series
Click here to see answer by mccravyedwin(407)

Question 1188477: what is the sigma notation for 4+9+16+25+36

Click here to see answer by ikleyn(52787)

Question 1188477: what is the sigma notation for 4+9+16+25+36

Click here to see answer by Solver92311(821)

Question 1188493: The 20th term is 26 and the common difference is -5. Find the 1st term and 15th term.
Click here to see answer by ikleyn(52787)

Question 1188493: The 20th term is 26 and the common difference is -5. Find the 1st term and 15th term.
Click here to see answer by MathTherapy(10552)

Question 1188494: 8, 20, 17, 10, 35, 5, _(?)_
what is the answer for question mark?

Click here to see answer by ikleyn(52787)

Question 1188532: 1/2,-4/5,27/8,-256/11 ......
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Question 1188532: 1/2,-4/5,27/8,-256/11 ......
Click here to see answer by greenestamps(13200)

Question 1188610: Calculate the 12^th Term of each of the sequence 1/3,1/6,1/12,1/24
Click here to see answer by MathLover1(20850)

Question 1189041: which number extends the series?
First Series: what's the next number?
7,9,14,23,37,60=?
Second Series:
8,16,24,38,62,100=?
Third Series:
4,7,15,29,59,117=?
Click here to see answer by greenestamps(13200)

Question 1189135: 6, 3 3/4, 2 1/4, 1 1/4, 3/4, 3/4, _____
answer key shows that the answer is 0, but I don't know how

Click here to see answer by greenestamps(13200)

Question 1189213: What is the next number in this sequence.
1,2,5,7,11,_,17
Click here to see answer by ikleyn(52787)

Question 1189392: The sum of the first four terms of a linear sequence (A.P) is 26 and that of the next four terms is 74.find the values of (i)the first term (ii)the common difference.
Click here to see answer by ikleyn(52787)

Question 1189532: Write the formula describing the sequence 6,14,22,30.
Click here to see answer by josgarithmetic(39617)

Question 1189532: Write the formula describing the sequence 6,14,22,30.
Click here to see answer by MathLover1(20850)

Question 1189544: Write Like If the given represents sequence, and Unlike if the given represents series.

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Question 1189706: Jorge buys a property on credit, having to pay it in 4 years, in the 1st year the monthly installments are US$ 660. In successive years the monthly installments suffer an increase of 3% in relation to with those of the previous year. What is the approx. of each monthly installment in the last year of payment? a) $700
b) 7215
c) $743
d) $765
Click here to see answer by Boreal(15235)

Question 1189812: A sequence has a term 0 of 125 and was decreasing by 6%. What is the explicit equation for this sequence?

Click here to see answer by ikleyn(52787)

Question 1189816: Find the number of terms in sequence 12;7;2;....;-203

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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