Number sequences mixed review

Learning Objectives Identify if a sequence is arithmetic, geometric, or quadratic. Determine the common difference (d), common ratio (r), or constant second difference for a given sequence. Apply the correct formula to find the nth term of an arithmetic or geometric sequence. Derive the nth term rule for a quadratic sequence of the form a_n = An^2 + Bn + C. Solve multi-step problems by first identifying the sequence type and then applying the appropriate methods. Compare the long-term behavior of different types of sequences. Ever notice how a stadium wave moves, or how your savings can grow over time? 🌊💰 These are real-life number sequences in action! This tutorial is a mixed review of the three main types of number sequences you've learned: arithmetic, geometric, a...

TermDefinitionExample SequenceAn ordered list of numbers, called terms, that follow a specific pattern or rule.2, 5, 8, 11, ... is a sequence. Arithmetic SequenceA sequence where the difference between any two consecutive terms is constant. You find the next term by adding or subtracting the same number.10, 7, 4, 1, ... (The constant difference is -3). Common Difference (d)The constant value added to each term to get the next term in an arithmetic sequence.In the sequence 5, 9, 13, 17, ..., the common difference, d, is 4. Geometric SequenceA sequence where the ratio between any two consecutive terms is constant. You find the next term by multiplying or dividing by the same number.2, 6, 18, 54, ... (The constant ratio is 3). Common Ratio (r)The constant value multiplied by each term to get...

Arithmetic Sequence nth Term Formula a_n = a_1 + (n-1)d Use this to find any term (a_n) in an arithmetic sequence. You need the first term (a_1), the term number you want to find (n), and the common difference (d). Geometric Sequence nth Term Formula a_n = a_1 \cdot r^{n-1} Use this to find any term (a_n) in a geometric sequence. You need the first term (a_1), the term number (n), and the common ratio (r). Quadratic Sequence General Form a_n = An^2 + Bn + C This is the general form for the rule of a quadratic sequence. The constant second difference is equal to 2A. You find B and C by solving a system of equations.