Number sequences mixed review

Learning Objectives Identify if a sequence is arithmetic, geometric, quadratic, or none of these. Determine the common difference, common ratio, or constant second difference of a sequence. Derive the explicit formula (nth term rule) for arithmetic, geometric, and quadratic sequences. Use a formula to find any specific term in a sequence. Determine a missing term within a given sequence. Distinguish between linear, exponential, and quadratic growth patterns as they relate to sequences. Apply sequence formulas to solve multi-step problems. If you get paid $2 on day one, $4 on day two, and $8 on day three, how much would you earn on day 30? 🤯 Let's find out how sequences can help you answer this! This tutorial is a mixed review of the different types of number sequenc...

TermDefinitionExample SequenceAn ordered list of numbers, called terms, that follow a specific pattern or rule.The list 5, 10, 15, 20, ... is a sequence. Arithmetic SequenceA sequence where the difference between any two consecutive terms is constant. This constant is called the common difference (d).In the sequence 4, 7, 10, 13, ..., the common difference is 3. Geometric SequenceA sequence where the ratio between any two consecutive terms is constant. This constant is called the common ratio (r).In the sequence 3, 6, 12, 24, ..., the common ratio is 2. Quadratic SequenceA sequence where the difference between consecutive terms (the first differences) forms an arithmetic sequence. The differences of these differences (the second differences) are constant and non-zero.For the sequence 1, 4...

Arithmetic Sequence Formula a_n = a_1 + (n-1)d Use this to find the nth term (a_n) of 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 Formula a_n = a_1 * r^(n-1) Use this to find the nth term (a_n) of a geometric sequence. You need the first term (a_1), the term number you want to find (n), and the common ratio (r). Quadratic Sequence Formula a_n = An^2 + Bn + C This is the general form for the nth term of a quadratic sequence. The coefficients A, B, and C are found by analyzing the first and second differences of the sequence.