Skip-counting puzzles

Learning Objectives Identify if a skip-counting puzzle represents a linear (arithmetic) or quadratic sequence. Calculate the first and second differences of a given sequence to determine its underlying pattern. Derive the nth term formula for any arithmetic sequence using algebraic methods. Derive the nth term formula for a quadratic sequence by solving a system of linear equations. Solve for missing terms in a sequence, including those involving radical expressions. Apply polynomial functions to model and predict future terms in complex skip-counting puzzles. If a pattern starts with 2, 9, 22, 41... what are the next two numbers and why? 🤔 This isn't your elementary school skip-counting! In this tutorial, we'll elevate the simple idea of skip-counting into a pow...

TermDefinitionExample Arithmetic SequenceA sequence of numbers where the difference between consecutive terms is constant. This is a linear pattern.The sequence 3, 7, 11, 15, ... is an arithmetic sequence because you add 4 each time. Common Difference (d)The constant value added to each term to get the next term in an arithmetic sequence.In the sequence 3, 7, 11, 15, ..., the common difference is d = 4. Quadratic SequenceA sequence of numbers where the 'second difference' between consecutive terms is constant. The general term is a quadratic polynomial of the form an²+bn+c.The sequence 2, 5, 10, 17, 26, ... is quadratic. The first differences are 3, 5, 7, 9 and the second differences are a constant 2. First DifferencesThe sequence formed by subtracting each term from the subsequ...

nth Term of an Arithmetic Sequence a_n = a_1 + (n-1)d Use this formula to find any term (a_n) in an arithmetic sequence. 'a_1' is the first term, 'n' is the term number you want to find, and 'd' is the common difference. nth Term of a Quadratic Sequence a_n = An^2 + Bn + C The general form for any quadratic sequence. You must find the coefficients A, B, and C by analyzing the sequence's differences and solving a system of equations. Finding Coefficients for a Quadratic Sequence 2A = (Second Difference) \\ 3A + B = (First term of the first differences) \\ A + B + C = (First term of the sequence) A system of equations used to find the coefficients A, B, and C for the quadratic formula a_n = An^2 + Bn + C. Solve for A first, then B, th...