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 1174075: Complete the following number sequence.
501 940,706 419,______,886 415,_______
Thank you.
Click here to see answer by ikleyn(52787)

Question 1174076: Complete the following number sequence.
_______,132 794, 208 941,______,360 729
Click here to see answer by ikleyn(52787)

Question 1174086: When computing for the check digit of a barcode why do we need to multiply the even-positioned digits by 3?
Click here to see answer by math_helper(2461)

Question 1174086: When computing for the check digit of a barcode why do we need to multiply the even-positioned digits by 3?
Click here to see answer by ikleyn(52787)

Question 1174212: The sum of 8th term of an A.P is 160 while the sum of the 20th term is 880
Find (a) 43rd term
(b) sum of the 12th term

Click here to see answer by ikleyn(52787)

Question 1174211: Find the missing number in the pattern?
1600,400,100, what’s next number?
Click here to see answer by ikleyn(52787)

Question 1174211: Find the missing number in the pattern?
1600,400,100, what’s next number?
Click here to see answer by josgarithmetic(39617)

Question 1174528: Write a rule for the nth term of the sequence. Use your rule to find a30. - 4, 5, 14, 23, 32, . . .

Click here to see answer by Boreal(15235)

Question 1174639: It is your job to make numbered tags for placing on 332
332
bicycles in your city. Tags are created by using stickers from 0 to 9 and placing them on a plastic surface. For example, you would create the tag number 313 by using a 3 sticker, a 1 sticker and then another 3 sticker.
In creating all of the tags, determine the number of 2’s
stickers you will use.

Click here to see answer by greenestamps(13200)

Question 1174724: The explicit formula for a sequence is an=5−7n. What is the value of a12
Click here to see answer by ikleyn(52787)

Question 1174904: Find the sum of the ap:
logx(27/8), + logx(9/4), + logx(3/2)...(10 terms)
Answer is 15 (logx 2 − logx 3)
Click here to see answer by math_tutor2020(3817)

Question 1175017: Find a formula for the nth triangular number Sn = 1 + 2 + 3 + · · · + n.
For what values of n is Sn: i: divisible by 5, ii: even?
Click here to see answer by ikleyn(52787)

Question 1175017: Find a formula for the nth triangular number Sn = 1 + 2 + 3 + · · · + n.
For what values of n is Sn: i: divisible by 5, ii: even?
Click here to see answer by math_helper(2461)

Question 1175058: find k so that 2k+1, 3k+1 and 5k+1 form a geometric sequence
Click here to see answer by ikleyn(52787)

Question 1175082: 18 a Find 1 + 2 + . . . + 24.
b Show that 1/n, 2/n + ... n/n = (n+1)/2
c Hence find the sum of the first 300 terms of
1/1 + 1/2 + 2/2 + 1/3 + 2/3 + 3/3 + 1/4 + 2/4 + 3/4 +4/4 + ....

Click here to see answer by ikleyn(52787)

Question 1175119: The series v + v^2 + v^3 + . . . has a limiting sum w.
a. Write w in terms of v.
b. Find v in terms of w.
c. Hence find the limiting sum of the series w − w^2 + w^3 − . . . , assuming that ∣w∣ < 1.
d. Test your results with v = 1/3
Click here to see answer by Edwin McCravy(20056)

Question 1175457: Find the arithmetic series whose 6th term is 0 and whose 10th term is 16. Show that there must be 14 terms in the series if its sum is 84.
Click here to see answer by ewatrrr(24785)

Question 1175520: What is the nth term of 5,10,15,20
Click here to see answer by ikleyn(52787)

Question 1175521: Please how do i solve the nth term for 5,10,15,20 i need answer so quickly
Click here to see answer by ikleyn(52787)

Question 1175544: Consider the arithmetic series
Click here to see answer by ikleyn(52787)

Question 1175605: 1. Evaluate the following sums given the sequence: 16, 14, 30, 44,...
F(1) + F(2) + F(3) = ______
F(1) + F(2) + F(3) + F(4) = _____
F(1) + F(2) + F(3) + F(4) + F(5) = _____
2. Determine the pattern in the successive sums from the previous question. What will be the sum of F(1) + F(2) + … + F(10)?
3. If you have a wooden board that is 0.75 meters wide, how long should you cut it such that the Golden Ratio is observed? Use 1.618034 as the value of the Golden Ratio. (
Click here to see answer by ikleyn(52787)

Question 1175646: Series and sequences in past question
Click here to see answer by ikleyn(52787)

Question 1175916: Marissa recently started working part time for a store that pays her $10.80 per hour. She is expected to work a total of 19 hours per week. She will have the following deductions made from her gross pay for the week:
Social Security (6.2%)
Medicare (1.2%)
State Income Tax (2.5%)
Federal Income Tax (12%)
How much will her net paycheck be for the week?
Click here to see answer by Boreal(15235)

Question 1176147: Need to find what ? Is based on the pattern of the numbers
-8, ?, 06, 10, 12
Click here to see answer by greenestamps(13200)

Question 1176147: Need to find what ? Is based on the pattern of the numbers
-8, ?, 06, 10, 12
Click here to see answer by josgarithmetic(39617)

Question 1176146: (a) Prove that if the roots of
x^3 + ax^2 + bx + c = 0 form an arithmetic sequence, then 2a^3 + 27c = 9ab.
(b) Prove that if 2a^3 + 27c = 9ab, then the roots of
x^3 + ax^2 + bx + c = 0 form an arithmetic sequence.
Click here to see answer by Edwin McCravy(20056)

Question 1176284: An arithmetic sequence is represented by the function f(n) =5+2(n - 1) what is the first term of the sequence

Click here to see answer by ewatrrr(24785)

Question 1176367: ) Let the sequence (an) be defined by
an+1 = an + 3n for n ≥ 1 and a1 = 6.
Prove by induction that
an > 5.
Click here to see answer by math_helper(2461)

Question 1176312: In a geometric progression the 5th term is 9 times the 3rd term and the sum of the 6th and 7th terms is 1944. Determine (a) the common ratio,(b) the 1st term
and (c) the sum of the 4th to 10th terms inclusive.
Click here to see answer by htmentor(1343)

Question 1176500: I was given an arithmetic series 3+7+11+15+19+23+27....
How do I find T1 and S1
Click here to see answer by ikleyn(52787)

Question 1176503: I was given an arithmetic series 3+7+11+15+19+23+27.......
How do I find T1 and S1
While also expressing T1 in terms of S1
Click here to see answer by ikleyn(52787)

Question 1176510: Find the 6th and 15th term of the A.P whose first is 6 and common difference is 7
Click here to see answer by MathLover1(20850)

Question 1176510: Find the 6th and 15th term of the A.P whose first is 6 and common difference is 7
Click here to see answer by Boreal(15235)

Question 1176530:
Click here to see answer by josgarithmetic(39617)

Question 1176631: Which number is missing from this sequence?
75 15 ? 5 15 3 13
Click here to see answer by MathLover1(20850)

Question 1176631: Which number is missing from this sequence?
75 15 ? 5 15 3 13
Click here to see answer by greenestamps(13200)

Question 1176684: good day! have a series of numbers and i just want to know if this is a valid sequence.. thanks!
1
3
7
8
21
49
76
224
467
514
1155
2683
5216
10544

Click here to see answer by Solver92311(821)

Question 1176668: A sequence of positive integers with a_1 = 1 and a_9 + a_{10} = 646 is formed so that the first three terms are in geometric progression, the second, third, and fourth terms are in arithmetic progression, and, in general, for all i>=1, the terms a_{2i - 1}, a_{2i}, a_{2i + 1} are in geometric progression, and the terms a_{2i}, a_{2i + 1}, and a_{2i + 2} are in arithmetic progression. Find the greatest term in this sequence that is less than 1000.

Click here to see answer by greenestamps(13200)

Question 1176729: A salesman receives $25 for every vacuum cleaner he sells. If he sells more than 10 vacuum cleaners, he will
receive an additional $1.75 for each successive sale until he is paid a maximum of $46 per vacuum cleaner. How
many must he sell to reach this maximum?
Click here to see answer by greenestamps(13200)

Question 1176803: If the man’s age is a 3-digit number, his age is equal to product of two numbers. One of the numbers is the sum of the digits and the other number is product of the digits his age is?
Click here to see answer by ikleyn(52787)

Question 1176795: If the man’s age is a 3-digit number, his age is equal to product of two
numbers. One of the numbers is the sum of the digits and the other number is
product of the digits his age is?
Click here to see answer by ikleyn(52787)

Question 1176766: Let |r| < 1,
S = sum_{k=0}^{infty} r^k,and
T = sum_{k=0}^{\infty} k r^k.
Our approach is to write T as a geometric series in terms of S and r.
Give a closed form expression for T in terms of r.
Click here to see answer by Solver92311(821)

Question 1177002: Find the coefficient of the term in the expansion of
Click here to see answer by Boreal(15235)

Question 1177003: Give an explicit rule for the nth term of the sequence:
-8, 3, 14, 25, ....
Click here to see answer by Boreal(15235)

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