Ask Dr. Math Strategies for Finding Sequences

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 Strategies for Finding Sequences, a selection of answers from the Dr. Math archives. Strategies for Tests on Sequences I have a problem answering test questions about number sequences. Nth Term in a Sequence Here is the sequence: 1, 2, 5, 14 ... Find the following 2 terms and a formula for the nth term. Solving a Sequence Write an expression to find the nth term of the following sequence: 3, 9, 18, 30, 45... Finding a Rule for a Sequence What is the next number in this sequence? 1, 3, 11, 67, ? Finding the Next Number in a Series Are there any formal or systematic methods for solving problems that ask you to find the next number in a series? Predicting the Next Number When given a series of numbers and asked to predict the next number, what is the formula for doing so? Describing Patterns in Sequences My students are able to identify the number patterns corresponding to number sequences, but are having difficulty explaining them in words. Finding Formulas for Number Sequences My question is about trying to find a formula between numbers. Formula for a Sequence A variety of techniques for solving problems like this one. Finding a Pattern Give the next four numbers in the sequence: 2, 8, 7, 28. Working with Sequences Give the next two terms of the sequence: 1, 1, 2, 4, 3, 9, ... 1, 7, 23, 55, 109, 191, ___ My family is stumped on this number pattern: 1,7,23,55,109,191,___ ... Sequence Differences 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? Completing Geometric Sequences How do you find the missing terms of a geometric sequence?