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 1157063: What is the sum of the arithmetic series below?
-100+-95+-90+-85+...+-5+0+5+...+85+90+95+100
Click here to see answer by MathLover1(20850)

Question 1157063: What is the sum of the arithmetic series below?
-100+-95+-90+-85+...+-5+0+5+...+85+90+95+100
Click here to see answer by my_user_id(3)

Question 1157234: Find a formula a(n) for the 𝑛- th term of the following sequence. Assume the series begins at 𝑛=1.
1/1, −1/4, 1/9, …
Click here to see answer by ikleyn(52787)

Question 1157257:
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Question 1157406: -2,-4,-12,-48,-240
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Question 1157487: sara says that 1008 is a term in the sequence 6, 9, 12, 15 explain why she is wrong
Click here to see answer by ikleyn(52787)

Question 1157937: The sum of the first three terms in a GP is 38. Their product is 1728. Find the values of the three terms.

My answer were 8 and 18. I want to confirm if it's correct and how will I find the values of the three terms with two solution of a and r
Click here to see answer by ikleyn(52787)

Question 1157939: The second and fifth term of a GP are 3/2 and 1/12, respectively. What is the first term?

Fr solving this question, I feel that there's a problem with the question. Do you agree pls.
Click here to see answer by josgarithmetic(39617)

Question 1157938: The first and 3rd terms of a GP are 2 and 1/9,respectively. Find:
a) the common ratio
b) the sum of the first 5 terms.
Click here to see answer by josgarithmetic(39617)

Question 1158075: what is the sequence/pattern 1, 3, 7, 15, 31

Click here to see answer by Alan3354(69443)

Question 1158164: find the term named in the problem, the explicit formula, and the recursive formula
http://prntscr.com/sbdhmp
Click here to see answer by MathLover1(20850)

Question 1158276: Express the following series using the sigma notation.
+ + ... + + ...

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Question 1158286: If John takes a loan for $5,000 with a monthly interest of 3%, and he pays $250 per month, what would be the balance after 1 month
Click here to see answer by solver91311(24713)

Question 1158296: Can you tell me what numbers come next in this sequence?
81, 27, , , 1, , Three numbers are missing
Click here to see answer by ikleyn(52787)

Question 1158303: A population of bacteria originates with 2500 bacteria. After a harmful substance is introduced into the environment, the rate of decline of the bacteria population is 10% per hour. In addition, 65 bacteria are added to the population each hour. How many bacteria are in the population after two hours.
Click here to see answer by Shin123(626)

Question 1158359: prove that (n 0) + (n 1) + (n 2) + ... + (n k) = 2^n is true using mathematical induction
note that (n k) is a falling factorial
Click here to see answer by Shin123(626)

Question 1158359: prove that (n 0) + (n 1) + (n 2) + ... + (n k) = 2^n is true using mathematical induction
note that (n k) is a falling factorial
Click here to see answer by ikleyn(52787)

Question 1158427: Consider the sequence.
4.5, −22.5, 112.5, −562.5, …
Click here to see answer by Shin123(626)

Question 1158427: Consider the sequence.
4.5, −22.5, 112.5, −562.5, …
Click here to see answer by Edwin McCravy(20056)

Question 1158365: prove that (n 0) + (n 1) + (n 2) + ... + (n k) = 2^n is true using mathematical induction.
note that (n k) is a falling factorial, and that n is a positive integer.
Click here to see answer by Shin123(626)

Question 1158457: given the first term and the common difference of an arithmetic sequence, find explicit rule and the 37th term
http://prntscr.com/sctyxf
Click here to see answer by ikleyn(52787)

Question 1158459: given two terms in an arithmetic sequence, find the explicit formula
http://prntscr.com/scu2dm
Click here to see answer by ikleyn(52787)

Question 1158458: given a term in an arithmetic sequence and the common difference, find the 52nd term and the explicit formula
http://prntscr.com/scu0c8
Click here to see answer by MathLover1(20850)

Question 1158456: given the first term and the common difference of an arithmetic sequence, find explicit rule and the 37th term
http://prntscr.com/scty4s
Click here to see answer by MathLover1(20850)

Question 1158455: find the term named in the problem, the explicit formula, and the recursive formula
http://prntscr.com/sctxmi
Click here to see answer by MathLover1(20850)

Question 1158532: how to find the 7th term of an arithmetic sequence with a1 = -81 and d=12
Click here to see answer by ikleyn(52787)

Question 1158704: Find the first six partial sums S1, S2, S3, S4, S5, S6 of the sequence whose nth term is given.
1, 5, 9, 13, . . .

Click here to see answer by MathLover1(20850)

Question 1158769: Find the indicated terms of the geometric sequence with the given description.
The third term is
1/3
and the sixth term is
−9.
Find the first and second terms.
first term

second term

Click here to see answer by josgarithmetic(39617)

Question 1158774: Find the partial sum Sn of the geometric sequence that satisfies the given conditions.
a = 7, r = 2, n = 5
Click here to see answer by ikleyn(52787)

Question 1158775: Find the sum.
1 + 4 + 16 + · · · + 65,536

Click here to see answer by ikleyn(52787)

Question 1158789: evaluate each geometric series described
http://prntscr.com/setnv4
Click here to see answer by ikleyn(52787)

Question 1158788: evaluate each geometric series described
http://prntscr.com/setiw2
Click here to see answer by ikleyn(52787)

Question 1158773: Find the indicated terms of the geometric sequence with the given description.
The common ratio is 0.75 and the fourth term is 864. Find the first three terms.
first term

second term

third term
Click here to see answer by Boreal(15235)

Question 1158766: Find the indicated term of the geometric sequence with the given description.
The first term of a geometric sequence is 15 and the second term is 6. Find the fourth term.

Click here to see answer by greenestamps(13200)

Question 1158910: find the sum of the following series
http://prntscr.com/sfiqj8
Click here to see answer by ikleyn(52787)

Question 1158908: find the sum of the following series
http://prntscr.com/sfipq3
Click here to see answer by ikleyn(52787)

Question 1158912: find the sum of the following arithmetic series and write in summation notation
http://prntscr.com/sfiszj
Click here to see answer by MathLover1(20850)

Question 1158911: find the sum of the following arithmetic series and write in summation notation
http://prntscr.com/sfire3
Click here to see answer by MathLover1(20850)

Question 1158967: Find the fifth term of the sequence.
a(n) = 4a[(sub)n-1]+3, a(1) = 3
(n-1) is in subscript after 4a. I hope that makes sense. I tried using some of the formulas that I was given in class and can't seem to find one that works for me. Thank you so much in advance. <3
Click here to see answer by solver91311(24713)

Question 1159038: evaluate each geometric series described
http://prntscr.com/sg4tmc
Click here to see answer by MathLover1(20850)

Question 1159032: find the sum of the infinite geometric series
http://prntscr.com/sg32q2
Click here to see answer by MathLover1(20850)

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