Number sequences: mixed review

Learning Objectives Identify whether a given sequence is arithmetic, geometric, or quadratic. Determine the common difference, common ratio, or constant second difference of a sequence. Derive the explicit formula for the nth term (a_n) for various types of sequences. Use formulas to find the value of a specific term in a sequence. Calculate the sum of a specified number of terms for finite arithmetic and geometric series. Apply knowledge of sequences to solve multi-step problems. If a bouncing ball returns to 80% of its previous height with each bounce, can you predict how high it will be on its 10th bounce? 🏀 Let's find out! This tutorial is a mixed review of the different types of number sequences you've learned about. We will focus on how to quickly identify...

TermDefinitionExample SequenceAn ordered list of numbers, called terms, that follow a specific pattern or rule.5, 10, 15, 20, ... is a sequence where each term is 5 more than the previous one. Arithmetic SequenceA sequence where the difference between any two consecutive terms is constant. This constant is called the common difference (d).2, 9, 16, 23, ... (The common difference, d, is 7). Geometric SequenceA sequence where the ratio between any two consecutive terms is constant. This constant is called the common ratio (r).3, 6, 12, 24, ... (The common ratio, r, is 2). Quadratic SequenceA sequence where the difference between consecutive terms (the first differences) forms an arithmetic sequence. This means the second differences are constant.1, 4, 9, 16, 25, ... (The terms are n^2. The...

Arithmetic Sequence nth Term a_n = a_1 + (n-1)d Use this formula to find the value of the nth term (a_n) of an arithmetic sequence. You need the first term (a_1), the term number (n), and the common difference (d). Geometric Sequence nth Term a_n = a_1 * r^(n-1) Use this formula to find the value of the nth term (a_n) of a geometric sequence. You need the first term (a_1), the term number (n), and the common ratio (r). Sum of a Finite Arithmetic Series S_n = n/2 * (a_1 + a_n) Use this to find the sum (S_n) of the first n terms of an arithmetic sequence. You need the number of terms (n), the first term (a_1), and the last term (a_n). Sum of a Finite Geometric Series S_n = a_1 * (1 - r^n) / (1 - r) Use this to find the sum (S_n) of the first n terms of a geomet...