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 549014: 1)If f(x) = ax2 + bx + a is divided by (x – b) a , b ≠ 0 , remainder is ‘a’ , then a is 2)L.C.M. of two numbers is 500, their HCF is 10. If one number is 20 , other number is 3)If a chord of circle with radius 5 cm subtends a right angle at the centre , then length of chord is 4)The remainder when x2 − 10x + 25 is divided by x − 5 is 5)The ratio of area and perimeter of a square is 2 : 1 , then area of circle with diameter equal to diagonal of square is Click here to see answer by solver91311(16877)

 Question 548999: CAN YOU GIVE ME SOME SEQUENCE AND SERIES QUESTION TO SOLVE AND GIVE YOU THE ANSWER Click here to see answer by mathie123(224)

 Question 549047: A girl spent 1/5 of her cash on stamps and twice as much on postcards and then had €1.00. How much had she to start? Click here to see answer by solver91311(16877)

 Question 548994: What is the next number in the sequence? 8,2,4,1,2,0.5,1,__ Click here to see answer by Edwin McCravy(8908)

 Question 549565: what is the formula for finding the number of diagonals in a shape e.g. triangle has 0 diagonals, quadrilateral has 2 diagonals, pentagon has 5 diagonals, hexagon has 9 diagonals, and so on. Click here to see answer by stanbon(57307)

 Question 549641: write an equation for the nth term of the geometeric sequence 9/16, 3/8, 1/4. Find the seventh term of this sequence. Click here to see answer by unlockmath(1599)

 Question 549757: Give an example of a sequence {an} satisfying that: {an} is monotonic, 0 lim(n tends to infinity)an = 1/2 Click here to see answer by KMST(1868)

 Question 549775: Let k > 0 be a constant and consider the important sequence {kn}. It’s behaviour as n tends to infinity will depend on the value of k. (i) State the behaviour of the sequence as n tends to infinity when k = 1 and when k = 0. (ii) Prove that if k > 1 then kn tends to infinity as n teds to infinity (hint: let k = 1 + t where t > 0 and use the fact that (1 + t)n > 1 + nt. (iii) Prove that if 0 < k < 1 then kn tends to 0 as n tends to infinity . Click here to see answer by richard1234(5390)

 Question 549647: In the arithmetic Sequence, the 11th term is 72(t(11)=72), and the 27th term is 96 (t(27)=96). A) Find the common Difference (generator). B)Find the initial Value, t(0). C) Write the rule for this sequence. Click here to see answer by KMST(1868)

 Question 549782: Given a geometric series with first term a > 0 and common ration r > 0 prove that a finite “sum to infinity” exists if and only if r < 1 and show that in this case the sum to infinity is . Click here to see answer by richard1234(5390)

 Question 549787: Give an example of a function that is continuous at all non-integer values but is discontinuous at all integer values. Prove the discontinuity property of your function. Click here to see answer by richard1234(5390)

 Question 549996: Can a function be continuous at one value of x and discontinuous at all other x E R? Explain your answer, giving proofs where appropriate. Click here to see answer by richard1234(5390)

 Question 550079: Find the 43rd term of the sequence: 12, 14, 16, 18,... Show all your work. Click here to see answer by prateekagrawal(56)

 Question 550089: prove that if k>1 then k^n→∞ an n→∞ there is a hint given. Hint:let k=1+t where t>0 and use the fact that (1+t)^n>1+nt prove that if k is between 0 and 1 then k^n tends to 0 as n tends to infinity Click here to see answer by richard1234(5390)

 Question 549553: what is the formula for this sequence 0, 2, 5, 9, 14, 20 ....... Click here to see answer by mathstutor458(57)

 Question 550239: the sum of a geometric series of 6 terms with ratio 2 is negative 189. what is the first term? Click here to see answer by TutorDelphia(193)

 Question 550440: write the first four teerms of the sequence for n = 1,2,3,and 4 f(n) = 9 a1 = Click here to see answer by JBarnum(2044)

 Question 550646: 1) 3(4x-7)=2(7x+13) 2) x+6 ____ = x-12 3 Click here to see answer by jim_thompson5910(28593)

 Question 550929: Direction: use one of the formulas for special series to find the sum of the series. 42 ∑ 1 i=1 1. 42 is on top of the symbol, i=1 is on bottom and 1 on right side. 2. 5 on top, n on right, n=1 on bottom. the answer is 15 but how? 3. 18 on top, i=1 on bottom, i on right. 4. 20 on top, k on right, k=1 on bottom 5. 6 on top, n^2 on right, n=1 on bottom. 6. 10 on top, i^2 on right, i=1 on bottom 7. 12 on top, i^2 on right, i=1 on bottom 8. 35 on top, k^2 on right, k=1 on bottom again all these problems are shown in this symbol: ∑ thanks for ur help and happy new year! please show ur work with each of the problems so i could understand it. thank you very much. Click here to see answer by Edwin McCravy(8908)

 Question 550990: Which pays more over the course of 10 days - \$100 per day for the 10 days or one dollar the first day, \$2.00 the second, \$4.00 the third, \$8.00 the fourth, etc., up to and including the 10th day? Please help me solve this problem from my text book and show steps please. Thanks! Click here to see answer by TutorDelphia(193)

 Question 550985: Which pays more over the course of 10 days - \$100 per day for the 10 days or one dollar the first day, \$2.00 the second, \$4.00 the third, \$8.00 the fourth, etc., up to and including the 10th day? Please help Click here to see answer by Theo(3458)

 Question 551085: for part (a) find the sum of the first n terms of the arithmetic series. for part (b) find n for the given sum Sn. 45. 3+8+13+18+23+... a. n=20 b. Sn=366 46. 50+42+34+26+18+... a. n=40 b. Sn=182 47. -10+(-5)+0+5+10+... a. n=19 b. Sn=375 48. 34+31+28+25+22+... a. n=32 b. Sn=-12 49. 2+9+16+23+30+... a. n=68 b. Sn=1661 50. 2+16+30+44+58+... a. n=24 b. Sn=2178 please show your work also so i know how to do it, thank you for ur help and happy new year! Click here to see answer by mathstutor458(57)
 Question 551085: for part (a) find the sum of the first n terms of the arithmetic series. for part (b) find n for the given sum Sn. 45. 3+8+13+18+23+... a. n=20 b. Sn=366 46. 50+42+34+26+18+... a. n=40 b. Sn=182 47. -10+(-5)+0+5+10+... a. n=19 b. Sn=375 48. 34+31+28+25+22+... a. n=32 b. Sn=-12 49. 2+9+16+23+30+... a. n=68 b. Sn=1661 50. 2+16+30+44+58+... a. n=24 b. Sn=2178 please show your work also so i know how to do it, thank you for ur help and happy new year! Click here to see answer by KMST(1868)

 Question 551067: a new car depreciates by 20% in its first year. Each succeeding year it depreciates by 10%. Assume the car is still in good working condition after 10 years. If the car costs \$25000, calculate te value of the car after 10 years. Express your answer to the nearest \$10 Click here to see answer by mathstutor458(57)

 Question 550087: (i)prove that if k>1 then k^n→∞ as n→∞ Hint:let k=1+t where t>0 and use the fact that (1+t)^n>1+nt prove if 0 Click here to see answer by richard1234(5390)

 Question 551230: If a=21 c=1 d=5 total=38 e=50 f=101 g=202 h=303 m=11 total=656 Then, ashish=? Click here to see answer by Alan3354(30993)

 Question 551648: Evaluate (z+y)/6 for z = 33 and y = 15 (z+y)/6= Click here to see answer by fcabanski(874)

 Question 552039: If a ball rebounds three-fifths as far as it falls, how far will it (vertically) travel before coming to rest if dropped 14 feet? Click here to see answer by Theo(3458)

 Question 552544: I need some help with some homework. I'm struggling with these four problems: 1. What is the twenty-fifth term of the arithmetic sequence with a1 = –1 and d = –10? 2.What is the twenty-ninth term of arithmetic sequence with a1 = 13 and d = –5/2? 3. What are the two arithmetic means between –13 and 8? 4. What is Sn for the arithmetic series with d = –4, an = 27, and n = 9? Thanks so much! Click here to see answer by AnlytcPhil(1276)

 Question 553542: A population of bacteria is growing according to the exponential model P=100e^70t, where P is the number of colonies and t is measured in hours. How many colonies are present initially? A. 2.72 B. 70 C. 100 D. 1000 Click here to see answer by rapaljer(4667)

 Question 553539: Which has the same value as (4+3i)^2 A. 7 B 7+24i C. 25 D. 25 + 24i Click here to see answer by rapaljer(4667)

 Question 553548: Find the x-intercept of the function f(x)=a^x+1 - 1 A. (0,0) B. (a, 0) C. (-1, 0) D. (a-1,0) Click here to see answer by rapaljer(4667)
 Question 553548: Find the x-intercept of the function f(x)=a^x+1 - 1 A. (0,0) B. (a, 0) C. (-1, 0) D. (a-1,0) Click here to see answer by stanbon(57307)

 Question 553545: When Katie was born her mother invested \$5000 in an account for her college savings. The interest rate is 3.5% compounded annually. To represent this, we can use the formula V = 5000(1+r)t where r represents the interest rate and t represents the time in years. How much will Katie have in her account when she turns 18? A. 5,175 B. 7,127 C. 9,287 D. 12,472 Click here to see answer by stanbon(57307)

 Question 554879: i need to find the nth term of a pattern with consecutive even numbers, ive tried many solutions but neither see to be working. please help. Click here to see answer by KMST(1868)