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

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Question 1165081: 4,9,
Click here to see answer by ikleyn(52788)

Question 1165077: On the first swing, the length of the arc through which a pendulum swings is 20 cm. The length of each successive swing is 4/5 of the preceding swing. What is the total distance the pendulum has traveled during the four swings
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Question 1165079: Linda starts a chain letter and sends it to three friends. Each of the three friends sends the letter to 3 other friends and the sequence is repeated. Assuming that no one breaks the chain, how many letters will have been sent from the first through the sixth mailings?
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Question 1165080: What distance will a golf ball travel if it is dropped from a height of 72 m, and if, after each fall, it rebounds 2/3 of the distance it fell?
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Question 1165076: What distance will a golf ball travel if it is dropped from a height of 72 m, and if, after each fall, it rebounds 2/3 of the distance it fell?

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Question 1165091: if an object falls from rest in a vacuum near sea level, then, approximately the distance fallen in the 1st second is 16 feet, and in each succeeding second the object falls 32 feet father than in the preceding second. How far does the object fall in 20 seconds?
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Question 1165212: Write the number sequence by following the given rule.
Start at 20, (+10, -5)
Click here to see answer by AnlytcPhil(1806)

Question 1165212: Write the number sequence by following the given rule.
Start at 20, (+10, -5)
Click here to see answer by Edwin McCravy(20056)

Question 1165280: the geometric sequence is 6250,1250,250,...,2 what term is 2?
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Question 1165314: The first three terms of a geometric sequence are as follows.
4, -20, 100
Find the next two terms of this sequence.
Give exact values (not decimal approximations).
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Question 1165450: Find two numbers whose product equals -144 and whose sum equals 7
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Question 1165510: What is the 58th term of sequence 540, 495,450?
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Question 1165510: What is the 58th term of sequence 540, 495,450?
Click here to see answer by Edwin McCravy(20056)

Question 1165508: What is the 58th term of the sequence 540, 495,459
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Question 1165473: Given f30=832,040 and f28=317,811,what us f29? Show your solution.
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Question 1165610: The 12th term of an A.P is -41 given that the first term is 3 find the 20th term
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Question 1165637: The number 42 can be written in three different ways as the sum of two or more consecutive positive integers.
42 = 13 + 14 +15
= 9 + 10 + 11 + 12
= 3 + 4 + 5 + 6 + 7 + 8 + 9
Is it possible to write 105 in eight different ways as the sum of two or more consecutive positive numbers?
Click here to see answer by greenestamps(13200)

Question 1165705: An arithmetic sequence starts 23, 36, 49, 62, …. What is the first term of the sequence to exceed 200,000?
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Question 1165703: In 2004, there were 3000 iguanas on Galapagos island. Since then, the population of Iguana on the island has increased by 5% each year. In what year will the population first exceed 10,000?
Click here to see answer by Theo(13342)

Question 1165708: 3,3,11,19,29,155
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Question 1165715: What is the correct answer of:60_42_14
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Question 1165988: is 11/2, 25/6, 17/6, 3/2, 1/6 arithmetic?

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Question 1165988: is 11/2, 25/6, 17/6, 3/2, 1/6 arithmetic?

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Question 1166115: If the 9th term in a geometric sequence is 45 927 and the common ratio is 3, then what is the first term?
A: 7
B: 6
C:9
D: 8
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Question 1166130: Calculate the sum of the first 6 terms of the geometric series with 3rd term 6 and common ratio 2/3
A:1330/243
B:211/6
C:665/18
D:66/729
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Question 1166132: Determine the sum of the first 15 terms of the arithmetic series whose 5th term is 4 and consecutive terms increase by 3.
options:
195
285
182
169
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Question 1166127: The 13th term of a sequence is 8, and the 17th term is 8. What is the 25th term?
A:4
B:25
C:8
D:0
Click here to see answer by ikleyn(52788)

Question 1166131: A man takes out a $20 000 bank loan that accrues 8% interest each year. A man decides to pay off only the interest each year, and deposit a different amount X into an interest account that earns him 4% interest each year.
a) If the man decides to pay off the loan in 10 years how much does he spend on interest alone?
b) How much should he deposit into the interest account each year so that at the end of 10 years he can pay back the initial $20 000?
c) How much has the man spent totally?
Click here to see answer by Theo(13342)

Question 1166157: 2 numbers whose product is -12 and sum is -4
Click here to see answer by Alan3354(69443)

Question 1166212: Tickets for a certain show were printed bearing numbers from 11 to 100. The odd number tickets were sold by receiving cents equal to thrice the number on the ticket while the even number tickets were issued by receiving cents equal to twice the number on the ticket. How much was received by the issuing agency?

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Question 1166284: what is th nth term and amt of 3,12,27,48
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Question 1166283: what is th nth term and amt of 3,12,27,48
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Question 1166308: A grid below contains one large square and four small squares with circles on each corner of the smaller squares. Show that, up to rotation and reflection, there is only one way to fill the empty circles with the numbers 1 to 9 so that the sums of the numbers at the vertices of all five squares are the same.
Link to figure/diagram:
https://imgur.com/xrRbfsu
Click here to see answer by solver91311(24713)

Question 1166362: GIVE WHAT IS ASKED IN THE PROBLEM. SHOW YOUR COMPLETE SOLUTION:
LINDA STARTS A CHAIN LETTER AND SENDS IT TO THREE FRIENDS. EACH OF THE FRIENDS SENDS THE LETTER TO 3 OTHER FRIENDS AND THE SEQUENCE IS REPEATED. ASSUMING THAT NO ONE BREAKS THE CHAIN, HOW MANY LETTERS WILL HAVE BEEN SENT FROM THE FIRST TO THE SIXTH MAILINGS?

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Question 1166408: What is the next three terms for each sequence.
1.4x-5,7x-3,10x-1,...
2.7,11,18,29,47,...
3.2,3,5,7,11,...
Click here to see answer by josgarithmetic(39618)

Question 1166432: Write a conjecture that describes the pattern in the sequence:
-4, -1, 2, 5, 8

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Question 1166461: 8, 15, 22, 29, 36
Which term of the sequence is equal to 126?
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Question 1166461: 8, 15, 22, 29, 36
Which term of the sequence is equal to 126?
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Question 1166515: The second term of the geometric sequence is 250, and the fifth term is 16. Find the seventh term.

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Question 1166526: Which of the following sets of numbers follow a sequence?
a.0.5,1,1.3,1.4
b.0.25,0.5,0.75
c.0.2,0.3,0.5
d.1,2,0.5
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Question 1166531: What is 7th the term of this series : 81,27,9,3,1,⅓, ?
Click here to see answer by josgarithmetic(39618)

Question 1166563: What is the missing number
11 5 8 ? 4
Click here to see answer by greenestamps(13200)

Question 1166626: Find the sum of the first six terms 1,3,5,7...
a.169
b.196
c.225
d.256

Click here to see answer by ikleyn(52788)

Question 1166726: Hello, I'm having a hard time finding the sequence of this number pattern. Please help me. Thank you in advance 😊
5*4 = 14
6*8 = 22
2*8 = 10
9*6 = __
Note: My teacher told me that the asterisk (*) can be any operation.
Click here to see answer by ikleyn(52788)

Question 1166729: Given the sequence{-1,3,7,11,...}, find a 25
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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