Questions on Algebra: Sequences of numbers, series and how to sum them answered by real tutors!

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Question 1166727: Hello, I'm having a hard time finding the sequence of this number pattern. Please help me. Thank you in advance 😊
5*4 = 17
6*8 = 22
2*8 = 10
9*6 = __
Note: My teacher told me that the asterisk (*) can be any operation.
Edit: I have written in my first question that 5*4=14, but it's actually 17 and not 14. Sorry.
Click here to see answer by Edwin McCravy(20056)

Question 1166803: What is the next number 32, 26, 8, 4
Click here to see answer by josgarithmetic(39618)

Question 1166951: For the arithmetic sequence with t7 = 0.6 and t12 = -0.4, find t20.
Click here to see answer by ikleyn(52788)

Question 1167016: What is the general term for sequence 2, -4, 8, -16, 32, ...

Click here to see answer by math_helper(2461)

Question 1167016: What is the general term for sequence 2, -4, 8, -16, 32, ...

Click here to see answer by ikleyn(52788)

Question 1167088: The differences between the terms of the geometric sequence are known: '[a2-a1=-6,a3-a2=12' Find the sum of the first ten terms of that sequence.
Click here to see answer by Theo(13342)

Question 1167109: 3, -6, 12, 4, 20, ?
7, 16, 8, 27, 9, ?
2, 7, 26, 101, 400, ?
7, 21, 8, 72, 9, ?
Click here to see answer by ikleyn(52788)

Question 1167120: I am given the first three and the last term for this sequence. I need to know the number of terms for this?
1-k, 1+k, 1+3k..., 1+19k
Click here to see answer by math_helper(2461)

Question 1167119: What are the first five terms 50th term of this sequence?
An=2a n-1 + 5 and A1=3
Click here to see answer by ikleyn(52788)

Question 1167181: The first three terms and the last term is given I need to know the number of terms.
The last term is a mixed number I tried to write it to the best ability.
1/3, 1/2, 2/3,..., 2 5/6

Click here to see answer by ikleyn(52788)

Question 1167323: which of the missing term in this arithmetic sequence 23, 18,13,8,3 ___, -7,-12?
Click here to see answer by ikleyn(52788)

Question 1167320: In a geometric sequence whose first three terms are 9, -6, 4, ..., which term is 1024/6561?
Click here to see answer by Boreal(15235)

Question 1167353: In this problem, you are stacking bricks. Every row contains one more brick than the row above it. The instructions say to determine a quadratic function to model the total number of bricks in the stack,f(x), given a number of rows, x. However, I'm unable to create a function that makes sense for this problem. I'm aware that the pattern is that every time a row is created it has 1 more brick than the previous (the one of above it) row. I need help creating the quadratic function.
Click here to see answer by htmentor(1343)

Question 1167377: The first three terms of the finite sequence 1, 1/x, 2, y form an arithmetic sequence, while the last three terms form a geometric sequence find the values of x and y.
Click here to see answer by ikleyn(52788)

Question 1167274: How do you write equation for this sequence 16, 28, 42, 56
Click here to see answer by Edwin McCravy(20056)

Question 1167607: An equilateral triangle has a side of 4 decimeters. A new triangle is formed by joining the midpoints of the sides. If this procedure is repeated 5 times, what is the perimeter and area of the sixth triangle?
Click here to see answer by solver91311(24713)

Question 1167608: Three distinct positive integers are in geometric progression. Find the smallest possible value of their sum.
Click here to see answer by ikleyn(52788)

Question 1167820: Hello...what rule could be here?
1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0...
i know if would be 1 0 1 0 1 0 1 0 1 0 would be a_n=1/2((-1)^(n+1)+1) and -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 a_n=1/2((-1)^(n+1)-1) but being stuck in finding solution for 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0... could you help me?
Click here to see answer by ikleyn(52788)

Question 1167873: 5,7,11,14, ,20
Click here to see answer by greenestamps(13200)

Question 1167955: What Will Come Next in the Following Series?
T S R T S R R S ___?___
Click here to see answer by ikleyn(52788)

Question 1168071: Find the sum of the first 50 terms for the sequence -8,-5, -2, 1, ....
Click here to see answer by ikleyn(52788)

Question 1168251: Fill in the missing numbers in this sequence
6. _ 12. 8. _. 12. 24. 16
Click here to see answer by greenestamps(13200)

Question 1168283: what is the first five terms and 50th term of this sequence.
An=2a n-1 + 5 and a1=3
Click here to see answer by greenestamps(13200)

Question 1168321: If S=3/2+5/4+7/8+...+(2n+1)/2^n+... where n=1, 2, 3, ..., then find the value of S.
Click here to see answer by math_helper(2461)

Question 1168361: (a) Compute the sum:101^2 - 97^2 + 93^2 - 89^2 + ...+ 5^2 - 1^2.
(b)
Compute the sum (a +(2n+1)d)^2- (a + (2n)d)^2 +(a + (2n-1)d)^2 - (a+(2n-2)d)^2 + ... + (a+d)^2 - a^2.
Can you please explain in detail?
Click here to see answer by ikleyn(52788)

Question 1168370: Compute the sum (a +(2n+1)d)^2- (a + (2n)d)^2 +(a + (2n-1)d)^2 - (a+(2n-2)d)^2 + ... + (a+d)^2 - a^2
I don't understand, can you explain in detail?
Click here to see answer by ikleyn(52788)

Question 1168533: A geometric sequence has four positive terms a1,a2,a3,a4. If a3/a1=9 and a1+a2=4/3, then what is a3?
Click here to see answer by josgarithmetic(39618)

Question 1168724: Find the formula an for the following sequences:
1. 3, 4, 5, 6, 7,…
2. 2, 5, 10, 17, 26,…
3. √3, 3, 3√3, 9,…
4. 4/1, 9/2, 16/3, 25/4,…
5. - ½, 1/3, -1/4,…
Click here to see answer by Boreal(15235)

Question 1168778: Determine if each of the following is a geometric sequence. If so, determine the common ratio.
1. 2, 4, 8, 16, 32, . . . .
2. 1, 5, 9, 13, 17, . . . .
3. 1, -1, 1, -1, 1, . . . .
4. 2, 2/3, 2/9, 2/27, 2/81, . . . .
Click here to see answer by ikleyn(52788)

Question 1168777: 1. Find a formula for the nth term of the following sequence: 4, 12, 36, 108, 324, . . . .
2. Find the 8th of the geometric sequence whose third term is 1/25 and whose sixth is 1/3125
3. What are the first five terms of the geometric sequence whose first term is a1 = 2 and whose
common ratio is r = 3.
4. Find the 10th term of the geometric sequence whose first term is 8 and whose common ratio is ¼.
Click here to see answer by htmentor(1343)

Question 1168725: PROBLEMS:
1. Find a formula for the nth term of the following sequence: 4, 12, 36, 108, 324, . . . .
2. Find the 8th of the geometric sequence whose third term is 1/25 and whose sixth is 1/3125
3. What are the first five terms of the geometric sequence whose first term is a1 = 2 and whose
common ratio is r = 3.
4. Find the 10th term of the geometric sequence whose first term is 8 and whose common ratio is ¼.
Determine if each of the following is a geometric sequence. If so, determine the common ratio.
1. 2, 4, 8, 16, 32, . . . .
2. 1, 5, 9, 13, 17, . . . .
3. 1, -1, 1, -1, 1, . . . .
4. 2, 2/3, 2/9, 2/27, 2/81, . . . .
Click here to see answer by Alan3354(69443)

Question 1168804: The question asks to find the number of terms
11+17+...+365
Click here to see answer by math_helper(2461)

Question 1168804: The question asks to find the number of terms
11+17+...+365
Click here to see answer by ikleyn(52788)

Question 1168814: The question asks to find the sum
8+14+20+...+278
Click here to see answer by Boreal(15235)

Question 1168814: The question asks to find the sum
8+14+20+...+278
Click here to see answer by ikleyn(52788)

Question 1168844: The question says to find the 10th term for the following
An=3n-3
Click here to see answer by MathLover1(20850)

Question 1168844: The question says to find the 10th term for the following
An=3n-3
Click here to see answer by ikleyn(52788)

Question 1168864: 8,4,20,9,3,15,6,6,? Solve the series

Click here to see answer by ikleyn(52788)

Question 1168952: The side of the square is 20 inches . A second square is formed by joining in the proper order , the midpoints of the sides of the first square. A third square is formed by joining the midpoints of the second square , and so on . Find the sum of the perimeters and areas up to the 7th square.

Click here to see answer by htmentor(1343)

Question 1169187: The sum of the first and 4th term of a G.P is -1575 while the sum of the 3rd and 6th term is -25200. Find the first term, common ratio, and the sum of the 4th to 20th term inclusive.
Click here to see answer by greenestamps(13200)

Question 1169266: A 12-wheeler truck is loaded with 13 piles of log. The bottom row contains 25 logs. Each of the remaining piles contains 2 logs less than the number of logs on a pile directly below it. Find the total weight of the logs carried by the truck if each log weighs 57kg.
I hope you can help me to solve this. I’ve already watched a lot of youtube videos but I still don’t get it :( Thank you so much!
Click here to see answer by ikleyn(52788)

Question 1169268: The leading mall in the Philippines has launched its raffle draw promo as part of the celebration of its 24th anniversary. A customer is entitled to one raffle entry for every single receipt purchase of P2,000. A total of 24 winners will be drawn--two winners each month from January to December. The winners for the month of January will be given P50,000 each. The prize increases by P50,000 monthly. How much money was allotted by the mall for the raffle draw prizes?
Click here to see answer by greenestamps(13200)

Question 1169384: Hello this is more of a questions where I just need an explanation and not the answer.
The question states
With Sn denoting the sum of the first n terms of an arithmetic sequence, we are given that S1=9 and S2=20.
Can you please explain to me what denoting means?

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