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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?
 LookandSay 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 ndegree
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 xaxis. 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?
 ArithmeticoGeometric 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+ca)/a, (c+ab)/b and (a+bc)/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 surefire 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?
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