Arithmetic Sequences ~adapted from Walch Education

Arithmetic sequences • An arithmetic sequence is a list of terms separated by a common difference, the number added to each consecutive term in an arithmetic sequence. • An arithmetic sequence is a linear function with a domain of positive consecutive integers in which the difference between any two consecutive terms is equal. • The rule for an arithmetic sequence can be expressed either explicitly or recursively.

Arithmetic sequences, continued. • The explicit rule for an arithmetic sequence is an = a 1 + (n – 1)d, where a 1 is the first term in the sequence, n is the term, d is the common difference, and an is the nth term in the sequence. • The recursive rule for an arithmetic sequence is an = an – 1 + d, where an is the nth term in the sequence, an – 1 is the previous term, and d is the common difference.

Practice • Write a linear function that corresponds to the following arithmetic sequence. ▫ 8, 1, – 6, – 13, …

Solve the Problem: • Find the common difference by subtracting two successive terms. 1 – 8 = – 7 • Identify the first term (a 1). a 1 = 8 • Write the explicit formula. an = a 1 + (n – 1)d an = 8 + (n – 1)(– 7)

Write the formula in function notation. Simplify the explicit formula �an = 8 – 7 n + 7 �an = – 7 n + 15 ƒ(x) = – 7 x + 15 Note: the domain of an arithmetic sequence is positive consecutive integers.