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

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 Algebra: Sequences of numbers, series and how to sum them Solvers Lessons Answers archive Quiz In Depth

 Question 379724: Find the nth term formula for the arithmetic sequence: 20,17,14,11 Click here to see answer by ewatrrr(10682)

 Question 379767: Find the 50th term of the sequence 5, -2, -9, -16.... Click here to see answer by ewatrrr(10682)

 Question 380157: Find the sum of the first n terms of the following arithmetic sequence. a1 = 2, d = 2; n = 5. Click here to see answer by rfadrogane(214)

 Question 380239: for the sequence 1,4,7,10... find its n term Click here to see answer by ewatrrr(10682)

 Question 380245: For the sequence an=(4)/(n+1), its first term is _____, its second term is _____, its third term is _____, its fourth term is _____, its 100th term is _____ Click here to see answer by ewatrrr(10682)

 Question 380243: For the sequence an=n+1, its first term is_____, second term is ____, third term is ____, fourth term is ____, its 100th term is ____ Click here to see answer by ewatrrr(10682)

 Question 379877: In a certain sequence, each term is equal to (3) times the pervious term. If the fifth term in the sequence is 27, what was the first term? Click here to see answer by ewatrrr(10682)

 Question 378767: in a geometric sequence the fourth term is 8 and the tenth term is 512. if common ratio is negative, find the first three terms. Click here to see answer by ewatrrr(10682)

 Question 376960: Find the 7th term of the geometric sequence −8, 4, −2, ... (a) by listing out the first terms of the sequence. (b) by using a formula for finding the nth term of a geometric sequence. Then a second one which is similar is finding the 10th term of the g.s. 3, 6, 12, ... (a) by listing out the first 10 terms of the sequence. (b) by using a formula for finding the nth term of a geometric sequence. Click here to see answer by ewatrrr(10682)

 Question 376555: what is the and what is the algebraical expression for the sequence. Click here to see answer by ewatrrr(10682)

 Question 374462: Find a(1) for the arithmetic series with S(7) = 287 and d = 12. I know the answer is 5, but don't know the formula for solving the problem. Click here to see answer by ewatrrr(10682)

 Question 380275: How do i find the sum of the infinite geometric series: .996+(.996)squared+(.996)cubed + ..... Click here to see answer by Fombitz(13828)

 Question 380464: The nth term is given,need help finding the first 4 terms, a8 and a12 an=(-1)n(2n+4) Need help finding the indicated term of this sequence an=7+150/n;a17 How do I prove that for every natural number n, 1+3+5...+(2n-1)=n2 How do I find the sum, if it exist 10+1+1/10+1/100... How do I find the sum of the first 14 terms of the geometric series 20-25+25/2... How do I find the indicated term 4,8,16,32 and the 17th term Click here to see answer by solver91311(17077)

 Question 380584: 1. Show that the sum of any two odd numbers is always an even number. 2. Show that the product of any two even numbers is divisible by four. Click here to see answer by ewatrrr(10682)

 Question 380955: find a number whose product with 9 is the same as it sum with 56 Click here to see answer by mananth(12270)

 Question 381489: What is the gerneral term (in sigma notation) of this Fourier series: -Pi/2 <= x < pi/2 x=pi pi/2 <= x < pi x=2pi-2x -pi<= x < =pi/2 x=2pi+2x Click here to see answer by stanbon(57982)

 Question 382110: what is the sum of terms if the first 8 terms are :15,19,23,27,31,35,39,43 Click here to see answer by user_dude2008(1861)

 Question 382111: what is the sum of terms if the first 12 terms are :2.6,3.1,3.6,4.1,4.6,5.1,5,6,6.1,6.6,7.1,7.6,8.1 Click here to see answer by user_dude2008(1861)

 Question 382298: What is the general formula for the following series. 5,9,18,34,59,95 Click here to see answer by stanbon(57982)
 Question 382298: What is the general formula for the following series. 5,9,18,34,59,95 Click here to see answer by Edwin McCravy(8999)

 Question 382537: The sum of two numbers is 135. The difference between them is 9. Find the numbers. Click here to see answer by nerdybill(7009)

 Question 382729: The sum of two numbers is 201 and the difference between them is 11. Find the two numbers. Click here to see answer by richard1234(5390)

 Question 383992: What are the next two numbers in the sequence: 1/32, 4/16, 9/8, 16/4? Click here to see answer by richard1234(5390)

 Question 384043: GIVEN THAT P(A)=0.3 AND P(B)=0.5, AND P(A AND B)=0.12, DETERMINE P(A|B) Click here to see answer by robertb(4012)

 Question 384236: Question: There are 9 horses in a race. In how many ways can the first 3 positions of the order of the finish occur. Assuming no ties. I did the 9*8*7*6.... method but not sure what next. I tried dividing by 6 but a mistake. Click here to see answer by Alan3354(31537)

 Question 384274: On a map, two cities are 1 1/2 in. apart. If 3/8 in. on the map represents 45 mi, find the number of miles between the two cities. Click here to see answer by rfer(12730)
 Question 384274: On a map, two cities are 1 1/2 in. apart. If 3/8 in. on the map represents 45 mi, find the number of miles between the two cities. Click here to see answer by stanbon(57982)

 Question 384316: Find the missing number: 5, 8, 6, 4, 4, 0, 8, ? I tried 3n-1. I started with n=2,then n=3, but it failed at n=4. I also tried the multiple of the difference of the numbers. the difference between 5&8 is 3, then multiply that by the difference between 8&6 which is 2; so (5-8)* (8-6)= 6. Then (8-6) * (6-4)=4, then (6-4) * (4-4)=0 That's where it failed. I also tried 2n-1 starting with n=3, but that failed also. I looked for a pattern in the difference between the numbers, like the triangular numbers or Fibonacci numbers but no luck. I don't know what else to try. Click here to see answer by richard1234(5390)

 Question 384386: Hi Please help, Obtain the Maclaurin series expansion about the point 0 for the function ln(x+1) as ln(x + 1) = x-x^2/2+x^3/3+(1)^n+1x^n/n + ...    Note that we cannot find a Maclaurin expansion of the function ln x since ln x does not exist at x = 0 and so cannot be differentiated at x = 0. Thank You in advance Matt Click here to see answer by richard1234(5390)

 Question 384539: What is the sum of 56 and 9 Click here to see answer by jim_thompson5910(28717)

 Question 385518: the sequence is 1/6,1,6,36. how do i find the explicit formula? what is the explicit formula? Click here to see answer by ewatrrr(10682)
 Question 385518: the sequence is 1/6,1,6,36. how do i find the explicit formula? what is the explicit formula? Click here to see answer by stanbon(57982)

 Question 385636: find the 30th term for these numbers 2,8,16,26 Click here to see answer by richard1234(5390)

 Question 385826: Find the next 3 numbers in the following pattern: 2/3, 2/5, 6/25, 18/125,... Click here to see answer by stanbon(57982)

 Question 386226: Hi! I have a couple of questions I need help with so I would love for step-by step solutions. Thanks! 1. Find he sum of the integers between 1 and 100 which are not divisible by 3 2. Three consecutive terms of an arithmetic sequence have a sun of 12 and a product of -80. Find the terms. 3. Each year a sales-person is paid a bonus of \$2000 which is banked into the same account which earns a fixed rate of interest of 6% p.a. with interest being payed annually. The amount at the end of each year in the account is calculated as follows: A(0) = 2000 A(1) = A(0) x 1.06 + 2000 A(2) = A(1) x 1.06 + 2000 etc. Find the total bank balance after 10 years. Assume no fees or charges 4. A ball takes 1 second to hit the ground when dropped. It then takes 90% of this time to rebound to its new height and this continues until the ball comes to a rest. a. Show that the total time of motion is given by 1+2(0.9)+2(0.9)^2+2(0.9)^3... b. Find S(n) in for the series in the set given in a. c. How long does it take for the ball to come to rest? Sorry for all the questions. There are four and the last one has three sub-problems. I really appreciate all the help! Click here to see answer by solver91311(17077)

 Question 386328: What are the next 3 numbers in this number sequence 12, 24, 36, 48, 510? I have tried adding multiples of 12. That doesn't work for 510. Do I just add 12 to 510 (522, 534,546)? Click here to see answer by solver91311(17077)

 Question 386743: you are training for a triathlon. In your training routine each week, you bike 5 times as far as run and run 4 times as far as you swim. one week you trained a total of 200 miles. how many miles did you swim that week? Click here to see answer by mananth(12270)

 Question 387119: how do i write an algebric expression that represent Sn for the sequence {3,6,9,12...} and find the ninth term of this sequence Click here to see answer by richard1234(5390)

 Question 387127: write an algebraic expression that represents Sn for each expression and find the ninth term of each sequence: 1.) {12,6,3,1.5,..} 2.) {1/2,1/3,1/4,1/5,..} 3.) {1,-2,3,-4,..} Click here to see answer by richard1234(5390)

 Question 387770: find the explicit formula and the 40th term 8,11,14,17... Click here to see answer by ewatrrr(10682)