Sequences: mixed review

Learning Objectives Distinguish between arithmetic, geometric, and other types of sequences. Determine the common difference or common ratio from a given sequence. Write the explicit formula for the nth term of an arithmetic or geometric sequence. By the end of a this lesson, students will be able to calculate the value of a specific term (a_n) in a sequence. Solve for the number of terms (n) in a finite sequence. Determine the formula for a sequence given two non-consecutive terms. 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? 🧐 This tutorial is a mixed review of arithmetic and geometric sequences. You will learn to identify different sequence types, apply the correct formulas to solve fo...

TermDefinitionExample SequenceAn ordered list of numbers, called terms, that follow a specific pattern or rule.3, 7, 11, 15, ... is a sequence where each term is 4 more than the previous one. Arithmetic SequenceA sequence in which the difference between consecutive terms is constant. This constant is called the common difference (d).The sequence 5, 2, -1, -4, ... is arithmetic because the common difference is -3 (2 - 5 = -3). Geometric SequenceA sequence in which the ratio between consecutive terms is constant. This constant is called the common ratio (r).The sequence 2, 6, 18, 54, ... is geometric because the common ratio is 3 (6 / 2 = 3). Term (a_n)An individual number in a sequence. `a_n` refers to the term in the nth position, where `a_1` is the first term.In the sequence 10, 20, 30,...

Nth Term of an Arithmetic Sequence a_n = a_1 + (n-1)d Use this formula to find any term (`a_n`) of an arithmetic sequence when you know the first term (`a_1`), the term's position (`n`), and the common difference (`d`). Nth Term of a Geometric Sequence a_n = a_1 * r^(n-1) Use this formula to find any term (`a_n`) of a geometric sequence when you know the first term (`a_1`), the term's position (`n`), and the common ratio (`r`).