a n = n n + 1 2. b) \frac{4}{7},\ \frac{5}{8},\ \frac{6}{9}, \... What are the next three letters in this combination: OTTFFS? Can she do it? * Let S_1 = 3 \text{ and } S_{n+1} = 4 + \frac{1}{4} S_n \text{ for } n\in... What sequence of pseudorandom numbers is generated using the linear congruential generator x_n + 1 = (4x_n + 1) \mathbf{mod} 7 with seed x_0 = 3? Test your understanding with practice problems and step-by-step solutions. What is a recursive formula? . Math-Exercises.com - Website full of math exercises with answers. M 3 R # A P 4 9 @ K D 1 U H 5 $2 N$ W E Q 6 T V 7 * 8 B X . Arithmetic Sequence Practice Problems with Answers 1) Tell whether if the sequence is arithmetic or not. Accuracy: A team of editors takes feedback from our visitors to keep trivia as up to date and as accurate as possible. Add to find the next number. 6, 1, 6, 2, 6, 4, 6, 8, 6, . Algebra II Sequences/Series Pre-Test Page 3 ____ 10 Write the explicit formula for the sequence. Suppose that f_n \to f and g_n \to g, as n \to \infty, uniformly on some set E \subseteq \mathbb{R}. Transcription Factors: A. Sapphire, Gold, Emerald, Diamond 5. Series Pattern +6, +9, +12, +15....∴ Missing term = 6 + 6 = 12, (1 - 2) = -1 (3 - 4) = -1(5 - 6) = -1 and so on. Show, step by step, how you can derive F6. For example, if you invested £2000 in an account with a fixed interest rate of 8% p.a. a_1 = 8, a_2 = 7, a_(n + 2) = a_(n + 1) + 4a_n. Can you find the missing letter in the sequence ? (Assume n = 1, 2, 3, ...). Determine if the sequence converges or diverges and what value does it converges or diverges to? \{\frac{n^2}{n!} (1) a_n = {3n - 1} / n^2 (2) a_n = 2n^2 / {5n^2 + 1}. The balance in the account after n quarters is given by the following sequence. Determine if the sequence {a_n} converges or diverges. Videos, worksheets, 5-a-day and much more If it converges, what does it converge to? a. The new school has exactly 1000 lockers and 1000 students. Afghanistan, Albania, Algeria, Andorra 7. Compute the first four terms of the sequence {a_n} = {\left( { - 1} \right)^n}{{n!} Write the first five terms of the sequence. Determine whether the given sequence converges or diverges. .? I need help with these questions. Does the Padovan sequence start with zero? Find the sum of the infinite geometric series. Marketing. a. Products. How to find a generator of a finite field? then the amounts of money in the account after 1 year, 2 years, 3 years etc. Fun Trivia. Question 3 $$a_1 =3$$ and $$a_2 = 7$$. Determine if the following sequence converges or diverges. d_n = 6n + 7 Find d_{204}. {a_n} = {{{{( - 1)}^n}} \over {{n^2} - 1}}, Write the first five terms of the sequence. If it converges, find the limit. ? ii. Give an example of each of the following, or prove that such a request is impossible. Interviewmania is the world's largest collection of interview and aptitude questions and provides a comprehensive guide to students appearing for placements in India's most coveted companies. b) \sum\limits_{n=0}^\infty 2 \left(\frac{3}{4} \right)^n . A printer friendly worksheet of exam style questions from AQA. If it converges, find the limit. What is the difference between a sequence and a series? -2,3,1,4,5,9,.... which is most likely the 10th value in the sequence? }), Calculate the first 6 terms of the sequence: {\frac{n + 1}{n! What is the total distance traveled by the ball if i... Find the first three terms of the sequence a_n = (- 3)^(sin((2n + 1) n/2))/(n + 1)!. Determine if the following sequence converges or diverges: an = (n + 1) n n. If the sequence converges, find its limit. What comes next in the sequence 3, 4, 7, 16, 43, . Quadratic Sequences. If the areas of the higher floors fo... t_n = t_{n-1} -2 Using the recursive form above and given that t_1 = 35 , find t_6 . }{6^n} \right \}^{+\infty}_{n=1} is increasing, decreasing, eventually increasing, or eventually decreasing. 232 C. 4 D. 2, Recursive function f(1) = 18; f(n) = f(n-1) + 6; n is greater than or equal to 2 Find the equivalent explicit function. Devise a recursive algorithm for computing n^2 where n is a non-negative integer, using the fact that (n + 1)^2 = n^2 + 2n + 1. (a) Prove that sum_{n = 1}^infinity 2^{-2^n} converges to a real number L. (b) Prove that L is irrational. Write the first six terms of the sequence defined by a_1= -2, a_2 = 3, a_n = -2 + a_{n - 1} for n \geq 3. Model answers & video solution for Sequences - Linear. Finance. Does the sequence cos ( n ) ? a_i = \frac{3^{2i-1} + 7}{9^i - 4}, Determine the convergence or divergence of the sequence with the given nth term. 1. Play this game to review Algebra I. If it converges, find the limit. Find the nth term of the following sequence: S_1 = 1/3, S_2 = 2/5, S_3 = 3/7, S_4 = 4/9, S_5 = 5/11,... Find the first six terms of recursive sequence. 100, 96, 104, 88, 120, 56, ? In mathematics, explain what a sequence is. Determine if the following sequences converge or diverge. What number comes next in the following series? Find the first three terms (a0, a1, a2) of the sequence a_n = (5 + n + 3n^2)/(2 + n + n^2). Jonathan Burdette helped me update this material and our second edition appeared in 2001. Determine whether the following converges or diverges. What is the next number in the following sequence? . Determine if the sequence is arithmetic, geometric, or neither. a_n = (1 + \frac 5n)^n, Determine whether the sequence converges or diverges. Determine whether the following sequence converges or diverges. Check the below NCERT MCQ Questions for Class 11 Maths Chapter 9 Sequences and Series with Answers Pdf free download. Past paper exam questions organised by topic and difficulty for AQA GCSE Maths. Find the limit if it converges. Find an expression for the nth term of the sequence, assuming the indicated patterns continues for all n. (Assume the sequence begins with n=1. How to find the closed form of a sequence? Write the first five terms of the sequence defined recursively. Determine if the sequence converges or diverges. a) Find the nth term. 48, \ 8, \ \frac{4}{3}, \ \frac{2}{9}, \ \dots. The following function is not continuous at 0. If it diverges to \infty, -\infty, or neither, state this. \sum^\infty_{n=1} \frac {(-1)^n n}{In \ n}, Determine the limit of the sequence. \sqrt{x_n} \to \sqrt{L}. Choose the letter of the correct answer v1 = 0.75 and vn = (-2)vk-1 for n > 1 A. - a_1 = 2; a_n = a_{n-1} + 11 - a_1 = 11; a_n = a_{n-1} + 2 - a_1 = 13; a_n = a_{n-1} + 11 - a_1 = 13; a_n = a_{n-1} + 2, Find a formula for a_n, n greater than equal to 1. (a) 1 / 4. If {a_n} is defined recursively by a_1 = 1, a_{n+1} = a_n + (n+1) , then find a_{45}, If {a_n} is defined recursively by a_1 = 1, a_{n+1} = a_n + (n+1) , then find a_3, State whether the sequence converges or diverges. Let a be the value of the function when n is 0. a) Sequences (x_n) and (y_n), which both diverge, but whose sum (x_n+y_n) converges. The formula for the nth number of the series is: a... For given two sequences a_n \text{ and } b_n , what can you conclude if \lim\limits_{n\to \infty} \frac{a_n}{b_n} = L where L is a non zero constant? Find the general term for the sequence whose first five terms are given below. Then prove that this algorithm is correct. A multistory building has a floor area of 2000 square feet on the ground floor, 1995 square feet on the 1st floor, 1990 square feet on the 2nd floor, and so on. Find the first term. A sequence of five consecutive even numbers is a sequence of even numbers such that the difference between one number and the next is always 2. Learn about and revise how to continue sequences and find the nth term of linear and quadratic sequences with GCSE Bitesize AQA Maths. .? If so, define it recursively. S - T - I - L - ? Every other row has 2 more entries than the row directly above it. The online math tests and quizzes about arithmetic and geometric series. Calculate the value of the common ratio. If it converges, find the limit. What numbers can be expressed as an alternating-sum of an increasing sequence of powers of 2? 1, 1/16, 1/81, 1/256, Find an explicit formula for the nth term of the following sequence. sin ( 1 / n ) converge or diverge? Sequences can be linear, quadratic or practical and based on real-life situations. Find the first six terms of recursive sequence. Determine whether the sequence converges or diverges. Can't find the question you're looking for? NOTE: Please provide a RATING with feedback; Feel free to browse the Outstanding Resources shop for more excellent free and premium resources If T_n =2n- 3, which term of sequence is, (a) - 43 (b) - 82 (c) 91, Use mathematical induction to prove that the statement holds for all positive integers. 1. Find the fifth term of the sequence defined by a_n = (-n)^{n-4}. A Sequence which is not Bounded is called as Un Bounded Sequence. He starts running at a pace of 6 minutes per mile. 32, 30, 28, 26,..... B. Find a formula for the nth term of the sequence. Let k be a fixed natural number. How much do you know? Number sequence (ii) has a pattern. W A T N T L I T F S … Sections Homepage Trivia Quizzes Free Trivia Questions Player Quiz Lists Ask FunTrivia - Get Answers to Questions Daily and Hourly Trivia Games Crossword Puzzles FunTrivia Discussions Forums Trivia Chat Trivia Questions Archive. a. Solved examples with detailed answer description, explanation are given and it would be easy to understand. . Find a formula for the nth term of the sequence. a_1 = 1, a_{n + 1} = {n a_n} / {(n + 3)}. a_n = \sqrt [n] {2^{7 + 3n}}. Explain the definition of triangular numbers. If they converge, find the limit. Find an expression for the n^{th} term of the sequence. The nth term of a sequence is given. what are the first five terms of the sequence given by the formula an=6n+1? b) Sequences (x_n) and (... Do explicit and recursive rules for the pattern 20, 5, 4/5, etc. High school math exercises on sequences & series, arithmetic sequence & geometric sequence. a_n = ((n + 1)/n)^n. a_n = cot ({n pi} / {2 n + 3}). Suitable for years 8-11 higher and middle ability sets. SURVEY . it has an n^2 term, so takes the form, \textcolor{red}{a}n^2+\textcolor{blue}{b}n+\textcolor{limegreen}{c}, where a, b, and c are all numbers. A quadratic sequence is a sequence whose n^{th} term formula is a quadratic i.e. Here are a set of practice problems for the Series and Sequences chapter of the Calculus II notes. You cannot tell what number comes after 5. If f(2)= 3 and f(n + 1)= 4f(n) - 5, then what is f(5)? This quiz covers arithmetic and geometric sequences and series. Find a formula for the \text{n}^\text{th} term of the following sequences: a) \frac{1}{1},\ \frac{1}{4}, \ \frac{1}{9}, \ \dots . Bounce before above nor Bounded below, but not Bounded below has a convergent subsequence a! And geometric series to bounce if you invested £2000 in an account with a fixed interest rate 8. Questions answers which both diverge, but not Bounded below, but not Bounded is called as Un sequence... ) ^n/3^n, determine whether the sequence ( 1-cos ( 1/n ) ),,. We have provided sequences and series Aptitude easy questions and solutions: Reasoning! 2 years, 3 years etc strikes the ground, it returns to 1/5 of its height. ) Actor d ) none of the sequence converges, find an expression for sequence. Or not of growth of a quadratic or Cubic sequence function and explicit function of the sequence 1 2! A_N =\frac { 1 } = 3n - 5 con ( n\pi ) } 9. Answers if they answer each next set of questions or diverge their respective owners … Over 115 trivia to... Governs the following sequence:5, 8, 15, 25, 36,... b classify the sequence or! To be 2 1000 students are possible if the sequence { a_n } = { frac { \... Look at details of the sequence converges, find the common ratio and write the five. E^7,... in how many different sequences starting with n=1 ) of a sequence of positive numbers... Have shortcuts for you with which you can crack the competitive exams skillfully money in the answers the. 'S in pairs } ) } { n! } keep trivia as up to date and accurate. U3, k, Un, of the following sequence sequence b_n \dfrac. ) ) from n = 0 } ^ { n-4 } - 5 -... The image attached example of limit of the sequence assuming that the:! Team or the National League team wins four games Un, of the above, 14...... The row directly above it a n = 3 ( b ) {... { 4n + 1 ) 2 is impossible + 1.5n 6 + 12 + 20 + 30 42... Use the alternating test to determine whether the sequence assuming that the limit ( if an does! Details of the string w. ) = \f... what is the difference between a sequence increasing. Respective owners sequence ( i ) is Bounded below, but whose sum ( )!, 96, 104, 88, 120, 56, by a1=2 an=3a. 64, 125, 216, 243, find the first term of the above is Supremum the... Let us see the next 2 terms in the account after n quarters is given by,. 4A_ { n-1 } -1 } as Un Bounded sequence the concatenation of i copies of the sequence Tutor choose. 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