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

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Question 1134530: Consider two functions: and the function f(x) shown in the table.
Which statements are true?
Select EACH correct answer.
Are my answers correct?
The table and my answers are in the link here: https://prnt.sc/mjf4na
Click here to see answer by mathsolverplus(88)

Question 1134464: A computer prints all of the integers from 1 to 3456. How many times does it print the integer 5?
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Question 1134773: The sum of the first five terms of an A.P is 36 and the sum of the next four terms is 90. find the A.P
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Question 1134782: The sum of two Integers is greater than 23. One integer is 5 less than 3 times the other. What are the least values of the Integers?
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Question 1134805: Given the sequence:2;5;8;....
1. If the pattern continues ,then write down the next two terms.
2. Prove that none of the terms of this sequence are perfect squares.
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Question 1134808: Determine the time taken in years,for a sum of money to double if the interest rate is 12,64%p.a compounded half-yearly.

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Question 1134810: The recursive rule for a sequence is shown.
an = an -1 + 7
a1 = 17
The question and my answer are in the link here: https://prnt.sc/mlcpsa
Click here to see answer by ikleyn(52788)

Question 1134811: The explicit rule for a sequence is
an = 14 -9n.
What is the recursive rule for the sequence?
The question and my answer are in the link here: https://prnt.sc/mlcqhb
Click here to see answer by ikleyn(52788)

Question 1134813: The sales of homes in a new development have been increasing. In January, 5 homes were sold, in February, 12 homes were sold. In March, 19 homes were sold. This pattern continued for the remainder of the year.
What is the explicit rule that can be used to find the number of homes sold in the nth month of the year?
Is my answer correct?
The question and my answer are in the link here: https://prnt.sc/mlcrqi
Click here to see answer by ikleyn(52788)

Question 1134815: When the town of Samuel Village first started its voluntary recycling program, 1200 of the town’s residence participated. The town predicts that the number of people participating in the recycling program will increase by 35% each year.
Which explicit rule can be used to determine the number of people participating in the program in the fifth year?
Is my answer correct?
The question and my answer are in the link here: https://prnt.sc/mlct0g
Click here to see answer by ikleyn(52788)

Question 1134820: the sum of five terms of an arithmetic progression is 10 and the sum of their squares is 380. find the first term and the common difference. please I saw the answer to a similar question but it wasn't clear...
Click here to see answer by ikleyn(52788)

Question 1134809: Angela wants to buy a house for 700000.she has a deposit of 50000 and take out a loan for the balance at a rate of 18% p.a compounded monthly
1.how much money must Angela
borrow from the bank?
2.calculate the monthly payment if she wishes to settle the loan in 15 years
3.Angela later won the lottery and wishes to settle the loan after the 50th payment.what is the outstanding balance?
Click here to see answer by Theo(13342)

Question 1134873: Evelyn took a job that paid $100 the first week. She was guaranteed a raise of 2% each week.
How much money will she make in all over 8 weeks?
Round the answer to the nearest cent.
Is my answer correct?
The question and my answer are in the link here: https://prnt.sc/mltevo
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Question 1134866: In a geometric progression series find the value of r if logr+logr^2+logr^4+logr^8+...+logr^32=63
Click here to see answer by Theo(13342)

Question 1134871: Andrew earns an allowance of $12 the first week, $17 the next week, $22 the following week, and so on.
How much will Andrew earn over the course of 10 weeks?
Is my answer correct?
The question and my answer are in the link here: https://prnt.sc/mlte8a
Click here to see answer by ikleyn(52788)

Question 1134870: Akim runs 1.75 miles on his first day of training for a road race. The next day, he increases his distance run by 0.25 miles. The day after that, he increases his distance run by another 0.25 miles, and so on.
What is the total number of miles Akim runs over the course of 18 days?
Is my answer correct?
The question and my answer are in the link here: https://prnt.sc/mltdwo
Click here to see answer by ikleyn(52788)

Question 1134869: The explicit rule for a sequence is an =
What is recursive rule for the sequence?
Is my answer correct?
The question and my answer are in the link here: https://prnt.sc/mltdfg
Click here to see answer by ikleyn(52788)

Question 1134872: On the first day of a measles outbreak at a school, 8 students were identified to have the measles. Each day for the following two weeks, the number of new cases doubled from those identified with the disease the day prior.
How many students are identified to have measles in all at the end of the 6th day of the outbreak?
Is my answer correct?
The question and my answer are in the link here: https://prnt.sc/mlteit
Click here to see answer by Theo(13342)

Question 1134888: Hi what are the next two numbers in the sequence;
15.2, 11.64, 8.16
Click here to see answer by greenestamps(13200)

Question 1134934: What is 4∑n=1 [100(-4)^n-1] equal to?
Is my answer correct?
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Question 1134933: What is 11∑n=1 (98 - 2n) equal to?
Is my answer correct?
The question and my answer are in the link here: https://prnt.sc/mm61zw
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Question 1134936: What are the coordinates of the hole in the graph of the function f(x) ?
f(x) = x^2 + 4x - 12/x - 2
Is my answer correct?
The question and my answer are in the link here: https://prnt.sc/mm6b6x
Click here to see answer by ikleyn(52788)

Question 1134943: The sum of an arithmetic series is 100 times the value of its first term, while the last term is 9 times the first term. Calculate the number of terms in the series if the first term is not equal to zero.
Click here to see answer by josmiceli(19441)

Question 1135188:
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Question 1135338: The sum of three numbers in G.P is 21 and the sum of their squares is 189.Find the numbers

Click here to see answer by MathLover1(20850)

Question 1135361: The sum of the first n terms of a G.P. is 255 and the sum of their reciprocal is 255/128. If the first term is 1. Find n and the common ratio.
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Question 1135371: The sum of the first three terms of a G.P. is 42 and the fourth term exceeds first term by 42.
Click here to see answer by greenestamps(13200)

Question 1135595: the second term of a geometric is 11 and the sum to infinity is 100, find the two possible values of the common ratio and the corresponding first terms
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Question 1135592: whats the next term in this sequence 12, 17, 22, 27
describe he pattern

whats the next term in this sequence 135, 45, 15, 5
describe he pattern

whats the next term in this sequence 1, 4, 9, 16
describe he pattern

whats the next term in this sequence 18, 15, 12, 9
describe he pattern

Click here to see answer by greenestamps(13200)

Question 1135591: whats the next term 12 17 22 27
describe the pattern

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Question 1135637: what is 44,35.26
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Question 1135676: The following sequence is given:-32;-28;-24;-20......2.1
Find the nth term in the sequence
Hence determine the 35th term
How many terms must be added together such that the sum of the numbers equal to zero
Express the sum of the first 40 terms in sigma notation
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Question 1135842: The sum of three terms of an A.P. is 21 and the product of the first and third exceeds the second term by 6, find the terms.
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Question 1135842: The sum of three terms of an A.P. is 21 and the product of the first and third exceeds the second term by 6, find the terms.
Click here to see answer by Boreal(15235)

Question 1135842: The sum of three terms of an A.P. is 21 and the product of the first and third exceeds the second term by 6, find the terms.
Click here to see answer by ikleyn(52788)

Question 1135842: The sum of three terms of an A.P. is 21 and the product of the first and third exceeds the second term by 6, find the terms.
Click here to see answer by greenestamps(13200)

Question 1135867: given the sequence 6,12,24,48....,3027, find the a number of terms in the sequence
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Question 1135935: the sum of the 1st and 2nd term of an application is 4 and 10th term is 19 find the fifth and sixth term
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Question 1135945: A principal wanted to inform everyone that school was cancelled . He call 2 teachers each of whom in turn call 2 other member and so on. This process is repeated 6 times. How many teachers including the principal work at this school

Click here to see answer by Boreal(15235)

Question 1135959: For the series 16, 24, 36, 54,... find S7.

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Question 1135959: For the series 16, 24, 36, 54,... find S7.

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Question 1135971: The sum of the 1st and 2nd term of an A.P is 4 and the 10th term is 19.find the sum of the 5th and 6th term
Click here to see answer by ikleyn(52788)

Question 1135974: table:
1 2 3 4 5 6 7 8 9 10 11
15, 14, 13.2, 14, 12, 12.5, 11.6, 11, 9.8
what does 10 and 11 equal to?
Click here to see answer by ikleyn(52788)

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