in both finite and infinite settings. Use recursion Modern States breakdown of formulas standards: “College P.A.S.A.3 Derive and use the formulas for the general term and summation of Algebra” CLEP finite Use summation preparation 35% P.A.S.A.3 or infinite arithmetic and geometric series, if they exist. notation Modules 20% P.A.S.A.1 / P.F.IF.A.8 a. Determine whether a given arithmetic or geometric series converges or Find the common 4.3 Sequences and 20% P.A.S.A.4 diverges. difference for an series 15% P.A.S.A.2 arithmetic sequence (matches up with 10% P.A.S.A.5 b. Find the sum of a given geometric series (both infinite and finite). sections 11-1, 11-2 Write terms of an and 11-3 of the c. Find the sum of a finite arithmetic series. arithmetic sequence textbook) Use the formula for 4.4 Factorials and Understand that series represent the approximation of a number when P.A.S.A.4 the general term of Binomial truncated; estimate truncation error in specific examples. an arithmetic Theorem in P.A.S.A.5KnowandapplytheBinomialTheoremfortheexpansionof(x+y)n sequence (matches up with powers of and for a positive integer where and are any numbers, with x y n, x y section 11-5 of the coefficients determined for example by Pascal’s Triangle. Use the formula for textbook) the sum of the first P.F.IF.A.8 Recognize that sequences are functions, sometimes defined terms of an n recursively, whose domain is a subset of the integers. For example, the Fibonacci arithmetic sequence sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + f(n - 1) for n 1. Find the common ≥ ratio of a geometric sequence terms of a geometric sequence Use the formula for the general term of a geometric sequence Use the formula for the sum of the first terms of a n geometric sequence
in both finite and infinite settings. P.A.S.A.3 Derive and use the formulas for the general term and summation of finite or infinite arithmetic and geometric series, if they exist. a. Determine whether a given arithmetic or geometric series converges or diverges. b. Find the sum of a given geometric series (both infinite and finite). c. Find the sum of a finite arithmetic series. P.A.S.A.4 Understand that series represent the approximation of a number when truncated; estimate truncation error in specific examples. P.A.S.A.5KnowandapplytheBinomialTheoremfortheexpansionof(x+y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. P.F.IF.A.8 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + f(n - 1) for n ≥ 1. Use recursion formulas Use summation notation Find the common difference for an arithmetic sequence Write terms of an arithmetic sequence Use the formula for the general term of an arithmetic sequence Use the formula for the sum of the first n terms of an arithmetic sequence Find the common ratio of a geometric sequence terms of a geometric sequence Use the formula for the general term of a geometric sequence Use the formula for the sum of the first n terms of a geometric sequence Modern States “College Algebra” CLEP preparation Modules 4.3 Sequences and series (matches up with sections 11-1, 11-2 and 11-3 of the textbook) 4.4 Factorials and Binomial Theorem (matches up with section 11-5 of the textbook) breakdown of standards: 35% P.A.S.A.3 20% P.A.S.A.1 / P.F.IF.A.8 20% P.A.S.A.4 15% P.A.S.A.2 10% P.A.S.A.5
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