Arithmetic Sequences: Recursive and Explicit Formulas, Study Guides, Projects, Research of Calculus

Download Arithmetic Sequences: Recursive and Explicit Formulas and more Study Guides, Projects, Research Calculus in PDF only on Docsity! Aim #87: What is an arithmetic sequence? Homework: Handout Do Now: Write the recursive formula and find the next term for: a. 2, 5, 8, 11, ... b. 8, 19, 30, 41, ... A sequence is called arithmetic if there is a real number, d, such that each term in the sequence is the sum of the previous term and d. Arithmetic sequences are often called "linear sequences." Write the recursive and explicit formula for the following sequences: a) 4, 6, 8, 10, ... b) -2, -3, -4, -5, ... Recursive: Recursive: Explicit: Explicit: To find a explicit formula for an arithmetic sequence: an = a1 + d(n - 1) where an is the value of the nth term, a1 is the first term, and d is the common difference. We then simplify to get the formula in the easiest form to work with. The recursive formula is an+1 = an + d 2) Given the following sequences, determine if they are arithmetic or not. If they are, find the common difference and determine a formula to find the nth term. a. 24, 20, 16, 12,... b. 3, 5, 9, 15, 23,... c. -2, -5, -8, -11, ... d. w+3, 3w+8, 5w+13, ... 1) Determine if each of the following formulas is recursive or explicit and then write out the first 5 terms. Write the other formula as well. a. an = 3n - 2, n ≥ 1 b. f(n+1) = f(n) - 8, f(1) = 15 c. an = an-1 + 3, a1 = -4 d. f(n) = -2n + 5, n ≥ 2