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 1177008: Find the sum of the infinite series:
∞
∑
k=1
Click here to see answer by ikleyn(52788)

Question 1177010: The 2nd and 5th term of a geometric progression are 1 and1/8 respectively find
Common ratio
8th term
First term
Sum of the first 8th term
Click here to see answer by ewatrrr(24785)

Question 1177007: Find the sum in terms of n for
n
∑
k=1
Given:
n
∑=
k=1
n
∑=
k=1
Click here to see answer by greenestamps(13200)

Question 1177005: Do the following sequences converge or diverge? If they converge, state the limit.
a.
b.
c.
Click here to see answer by mccravyedwin(407)

Question 1177060: The closed form sum of
12 [ 1^2 * 2 + 2^2 * 3 + ... + n^2 (n+1) ]
for n <= 1 is n(n+1)(n+2)(an+b). Find an + b.
Click here to see answer by greenestamps(13200)

Question 1177105: given sequence 2;5;8
2.1.1 if the pattern continues
, then write down the next two terms
2.2.2 prove that none of the terms of this sequence are perfect squares

Click here to see answer by MathLover1(20850)

Question 1177107: consider the sequence of numbers: 2;5;2;9;2;13;2;17
calculate the sum of the first 100 terms of the sequence
Click here to see answer by mccravyedwin(407)

Question 1177107: consider the sequence of numbers: 2;5;2;9;2;13;2;17
calculate the sum of the first 100 terms of the sequence
Click here to see answer by MathLover1(20850)

Question 1177112: 1;3;5 are the first three terms of the first difference of a quadratic sequence. the 7th term of the quadratic sequence is 35
1.2.1 determine the 6th and 5th terms of the quadratic sequence
1.2.2 determine the nth term of the quadratic sequence
Click here to see answer by greenestamps(13200)

Question 1177109: a quadratic pattern has a second term equal to 1, a third term equal to -6 and fifth term equal to -14
1.1.1 calculate the second difference of this quadratic pattern
1.1.2 hence or otherwise, calculate the first term of the pattern

Click here to see answer by greenestamps(13200)

Question 1177181: The sum of n terms of a certain series is for all values of n. Fine the nth term and show that the series is an arithmetical progressim.
Click here to see answer by ikleyn(52788)

Question 1177330: Consider the sequence 6,6,2,-6,-18....show that -6838 is in the sequence
Click here to see answer by MathLover1(20850)

Question 1177555: Please I will Cashapp 10$ If anyone can solve it it's due today I really need help.
Pick DIFFERENT values that meet each description.
m = ____ (m is an integer and m<-10) d = ____ (d is an integer and -10 < d < -1)
n = ____ (n is an integer and n > 20) r = ____ (r is a rational # and 0 < r < 1)

1) Create an arithmetic sequence with a common difference of d, and the third term in the sequence is m. Show the first 5 terms of the sequence.

2) Write the explicit rule for the sequence that you created. Use your rule to confirm the 5th term of the sequence.

3) Write the recursive rule for your arithmetic sequence.

4) Use the formula for arithmetic series, and find the sum of the first 10 terms of the sequence that you created.

Part 2:
1) Using your chosen value of n, create a geometric sequence with a common ratio of r, and the first term of the sequence is n. Show the first 5 terms of the sequence.

2) Write the explicit rule for the sequence that you created. Use your rule to find the 10th term of the sequence.

3) Write the recursive rule for your geometric sequence.

4) Write a summation notation that depicts the sum of the first 25 terms of the geometric series. Find the sum. (Round to 5 decimal places if necessary.)

Click here to see answer by Boreal(15235)

Question 1177677: According to the following sequence how to find the nth term
1, 2, 3, 6, 11, 20, 37, 68, …
Click here to see answer by greenestamps(13200)

Question 1177696: Sequence and series
find the first four terms of the sequence 5n-7/2n

Click here to see answer by ikleyn(52788)

Question 1177695: Sequence and series
find the first four terms of the sequence 5n-7/2

Click here to see answer by ikleyn(52788)

Question 1177822: the sum of two numbers is 6. five times the larger number plus four times the smaller number is 44. find the numbers.
Click here to see answer by josgarithmetic(39618)

Question 1178050: The 6th term of an AP is 35 and the 13term is 77calculate S6-S4?

Click here to see answer by MathLover1(20850)

Question 1178050: The 6th term of an AP is 35 and the 13term is 77calculate S6-S4?

Click here to see answer by chhavi_1997(1)

Question 1178050: The 6th term of an AP is 35 and the 13term is 77calculate S6-S4?

Click here to see answer by ikleyn(52788)

Question 1178154: Consider each given sequence start. i) Classify each as arithmetic, geometric, and/or none of these. ii) Find the 28th term. iii) Find the sum of the first 7 terms, call it S7 .
88,83, 78, 73,
Click here to see answer by mananth(16946)

Question 1178152: Consider each given sequence start. i) Classify each as arithmetic, geometric, and/or none of these. ii) Find the 28th term. iii) Find the sum of the first 7 terms, call it S7 .

a) 44, −6, 44, −4,

Click here to see answer by MathLover1(20850)

Question 1178155: Consider each given sequence start. i) Classify each as arithmetic, geometric, and/or none of these. iii) Find the sum of the first 7 terms, call it S7 .
x x, 3 −1, 9x+ 2, 27x−3,
Click here to see answer by ikleyn(52788)

Question 1178153: Consider each given sequence start. i) Classify each as arithmetic, geometric, and/or none of these. ii) Find the 28th term. iii) Find the sum of the first 7 terms, call it S7 .
b) 34 2, ,3,6,3
Click here to see answer by ikleyn(52788)

Question 1178380: The sum to n terms of a sequence of numbers is given as : Sn = n/2(5n+9)
1. Calculate the 23rd term of the sequence
Click here to see answer by ikleyn(52788)

Question 1178650: a1= 200 d= 40
Click here to see answer by MathLover1(20850)

Question 1178650: a1= 200 d= 40
Click here to see answer by ikleyn(52788)

Question 1178663: fill in the blank of the sequence and the recursive definition
1 3
3 8
7 18
those are the term number so im missing 2,4,5,6

3, ,8, , , ,18
Click here to see answer by MathLover1(20850)

Question 1178674: The sixth and eighth terms of an arithmetic sequence are
−11 and −19.
Find the fifteenth term.
Click here to see answer by MathLover1(20850)

Question 1178674: The sixth and eighth terms of an arithmetic sequence are
−11 and −19.
Find the fifteenth term.
Click here to see answer by ikleyn(52788)

Question 1178672: Find the 9th, 24th, and nth terms of the arithmetic sequence.
3,1,-1.....
Click here to see answer by ikleyn(52788)

Question 1178669: Write the given series in summation notation.

1/1+1/4+1/9+1/16+1/25+1/36
Click here to see answer by ikleyn(52788)

Question 1178671: Write the given series in summation notation.
1-3/4+9/16-27/64+81/256-243/1024
Click here to see answer by ikleyn(52788)

Question 1178677: The seating section in a theater has 19 seats in the first row, 21 seats in the second row, and so on, increasing by 2 seats each row for a total of 10 rows. How many seats are in the tenth row, and how many seats are there in the section?
Click here to see answer by greenestamps(13200)

Question 1178675: Find the nth partial sum of the arithmetic sequence.
an = 7n + 2; n = 10
Click here to see answer by MathLover1(20850)

Question 1178670: Write the given series in summation notation.
3 − 9 + 27 − 81 + 243 − 729 + 2187
Click here to see answer by math_helper(2461)

Question 1178676: Find the nth partial sum of the arithmetic sequence.
an = 2n − x; n = 19
Click here to see answer by MathLover1(20850)

Question 1178673: Find the 9th, 24th, and nth terms of the arithmetic sequence.
a, a + 6, a + 12, ...
Click here to see answer by mananth(16946)

Question 1178646: A four-digit number abcd is called cool if a is divisible by 4, the two-digit number ab is divisible by 5, the three-digit number abc is divisible by 6 and abcd is divisible by 7. How many cool numbers are there where 8 is not one of the digits?
Click here to see answer by greenestamps(13200)

Question 1178668: Find the first three terms of the recursively defined sequence.
a1 = 5, a(n) = na(n−1)
Click here to see answer by greenestamps(13200)

Question 1178884: Write the rational number as the quotient of two integers in simplest form.
0.354
Click here to see answer by ikleyn(52788)

Question 1178890: Find the nth term of the geometric sequence.
3, 27, 243,
Click here to see answer by josgarithmetic(39618)

Question 1178890: Find the nth term of the geometric sequence.
3, 27, 243,
Click here to see answer by ikleyn(52788)

Question 1178889: Find the nth term of the geometric sequence.
−5, 20, −80,
Click here to see answer by josgarithmetic(39618)

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