Ask Dr. Math High School Archive

Dr. Math Home || Elementary || Middle School || High School || College || Dr. Math FAQ

 TOPICS This page:   sequences/series    Search   Dr. Math See also the Dr. Math FAQ:   golden ratio,   Fibonacci sequence Internet Library:   sequences/sets HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry Browse High School Sequences, Series Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     Strategies for finding sequences. Adding Arithmetic Sequences [07/10/1998] How do you add the numbers from 1 to 5000 without actually doing it or using a calculator? What if you were adding just the odd numbers? Calculating the Fibonacci Sequence [11/28/1996] Is there a formula to calculate the nth Fibonacci number? Decimal To Fraction Conversion [06/25/1998] I am trying to find a method (one that can be programmed on a PC) to convert the decimal part of a real number to a fraction represented by integers for the numerator and denominator. Describing Patterns in Sequences [04/16/2002] My students are able to identify the number patterns corresponding to number sequences, but are having difficulty explaining them in words. Doubling Grains of Wheat [10/7/1996] A man asked for 1 grain of wheat for the 1st square on a chess board, 2 grains for the 2nd square... Doubling Sequence [8/24/1996] On Jan 1st it snowed one centimeter; on Jan 2, 2cm; on Jan 3, 4 cm... Fibonacci and Incoming Bits [09/08/99] Given a transmitter sending 100 bits of random data over an ideal communication channel, what is the probability that there will be three consecutive 1's at least once in the sequence? Finding a Pattern [11/11/2001] Give the next four numbers in the sequence: 2, 8, 7, 28. Finding a Rule for a Sequence [07/24/2003] What is the next number in this sequence? 1, 3, 11, 67, ? Finding Sum Formula using Sequences of Differences [06/28/1998] Finding a formula for the sum of the first n fourth powers using sequences of differences. Finding the Pattern in a Series of Numbers [11/14/1995] What is the pattern for 1, 8, 27...? Infinite square root [6/4/1996] If y= sqrt(2+ sqrt(2+ sqrt(2+ sqrt(2+ ..., y=2,... how can I prove that this is true, using normal properties of roots? Look-and-Say Sequence [02/14/2002] I can't find the next six numbers: 1, 11, 21, 1211, 111221, ... Mean Proportionals and Geometric Means [01/06/1999] How do you find the mean proportional of two numbers? What about two mean proportionals? n mean proportionals? Next Number in a Sequence [03/13/2002] Given any sequence, one can construct an infinite number of n-degree polynomials that satisfy the sequence, hence discern an infinite number of answers. What is the proof for this? Sequence Differences [06/24/2003] The third and fourth terms of a sequence are 26 and 40. If the second differences are a constant 4, what are the first five terms of the sequence? Strategies for Tests on Sequences [7/9/1996] I have a problem answering test questions about number sequences. Sum of n Odd Numbers [7/11/1996] Why is the sum of the first n odd numbers the square of n? The Traveling Bee [09/18/1998] If a bee travels between two trains that are moving at 30 and 20 mi/hr respectively, starting from 50 mi apart, how far does the bee travel? Unsolvable Equations [11/10/2001] If I have an equation in the form of x^n+y^n=z, how do I solve for n? Why is Zero the Limit? [02/25/2002] Why is zero called the limit of the terms in the sequence the limit of 1 over n, as n approaches infinity, equals zero? 121, 111211, 311221 Puzzle (Look and Say Sequence) [10/23/2001] 121, 111211, 311221 - what's the next number? 1 + 2 + 3 + 4 + ... Equals ... -1/12?! [09/18/2012] Doctor Vogler explains how functions extended by analytic continuation can be evaluated to produce counterintuitive results. 1, 7, 23, 55, 109, 191, ___ [10/03/2002] My family is stumped on this number pattern: 1,7,23,55,109,191,___ ... 21^100 - Last Two Digits [09/04/1997] What are the last two digits of 21 to the 100th power? 22/7 as an Approximation for Pi [04/01/1998] Approximating pi by simple continued fractions. Activities to Find Pi [10/07/1998] Can you suggest any classroom activities to find pi, other than the standard way of measuring the circumferences and diameters of circles? Advanced Algebra [09/23/1997] My teacher gave us this problem: 1+1/(1+1/(1+1/(1+1/1+...))) Alternating Harmonic Series [11/18/1997] I am trying to find the proof for the sum of the alternating harmonic series. I did find out that it is ln(2), but please tell me why? Alternating Sequence [01/27/1997] Find a pattern and the next three numbers in the sequence: 0, 8, 27... Ant Walking in a Squared Spiral [06/02/1999] An ant walks out a distance of 1 from the origin, down the x-axis. It then turns left and goes up 1/2. If it continues turning left and going the half the previous distance, where does the ant end up? Are All Infinitely Long Repeating Numbers Even? [06/06/2000] Given an infinitely long repeating series, x = 12341234..., then 10000x = 123412341234... Since 9999 is odd and 12340000... is even, can we say that x is even, and therefore all infinitely long repeating series are even? Arithmetical Progression [7/7/1996] An arithmetical progression has a common difference of 1/1/2. The sum of the first n terms is 365 and the sum of the first 2n terms is 1330. Calculate the value of n and the first term. Arithmetic and Geometric Progressions [03/23/1998] Given a set of conditions, can you find a specific term in an arithmetic or geometric progression? Arithmetico-Geometric Series and Polylogarithms [07/06/2006] Is there a closed form expression for the sum of the series e^(-x) + 1/9 * e^(-3x) + 1/25 * e^(-5x) + 1/49 * e^(-7x) + ... ? Arithmetic Progression [12/19/1996] If (b+c-a)/a, (c+a-b)/b and (a+b-c)/c are in arithmetic progression, show that 1/a, 1/b and 1/c are also in arithmetic progression. Arithmetic Sequence Conundrum [10/11/2002] For some real number T, the first three terms of an arithmetic sequence are 2T, 5T - 1, and 6T + 2. What is the numerical value of the fourth term? Arithmetic Sequences as Lines [09/05/2003] In a sequence like -40, -25, -10, 5, ... is there a sure-fire way to find the the general term? Arithmetic Series [5/19/1996] How do you calculate a series like 2,4,6,8... for say 3 terms starting anywhere in the series not by adding 3 specific terms together, but by using the first term and the number 3? Arithmetic vs. Exponential Increases [05/06/1999] What does "....the work produced... will increase exponentially rather than arithmetically" mean? Page:  1  2  3  4  5  6  7  8  9 [next>]

Search the Dr. Math Library:

 Search: entire archive just High School Sequences, Series Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words