series and sequence formula

Sequences and Series - A sequence is an ordered listing of numbers such as {1, 3, 5, 7, 9}. In mathematical terms, a sequence is a function whose domain is the natural number set {1, 2, 3, 4, 5, …}, or some subset of the..

Sequences and Series - A sequence is an ordered listing of numbers such as {1, 3, 5, 7, 9}. In mathematical terms, a sequence is a function whose domain is the natural number set {1, 2, 3, 4, 5, …}, or some subset of the natural numbers, and whose range is the set of real numbers or some subset thereof. Let f denote the sequence {1, 3, 5, 7, 9}. Then f (1) = 1, f (2) = 3, f (3) = 5, f (4) = 7, and f (5) = 9. Here the domain of f is {1, 2, 3, 4, 5} and the range is {1, 3, 5, 7, 9}...

  Sequences & Series: Arithmetic Sequenceswww.mindbites.com This 74 minute sequences & series lesson begins with the terminology of a sequence and will show you how to use the general term formula to find any term of an arithmetic sequence as well as: - find the first term - find common difference - find number of terms - find & insert arithmetic means - determine if the series is finite or infinite Example Question: If x + 4, 3x, x^2 are the first three terms in an arithmetic sequence, find the sequence. Thislesson contains ...

  Sequences & Series: Geometric Sequenceswww.mindbites.com This 78 minute sequences & series lesson will show you how to use the general term formula to find any term in a geometric sequence as well as how to: - identify a geometric sequence - find the common ratio, the first term, the number of terms - find and insert geometric means - find a specific term - use a system of equations to solve problems Sample question: Insert 3 geometric means between 8 and 1/2. Thislesson contains explanations of the concepts and 20 example questions with step by step solutions plus 7 interactive review questions with solutions. Lessons that will help you with the fundamentals of this lesson include: - 085 Fractions (www.mindbites.com - 115 The 5 Basic Exponent Laws (www.mindbites.com - 160 Operations With Radicals (www.mindbites.com - 165 The zero, Negative and Rational Exponents (www.mindbites.com - 230 Solving Quadratic Equations by Factoring (www.mindbites.com

Question : Hi, I'm having some trouble with these. These are just to refresh my memory but I lost my notes and am trying to remember! 1) Find the sum of the n terms of the arithmetic sequence a1 = 7, a12 = 29 and n = 12. 2) Find the sum of the first 50 terms 1, 8, 15... using the sum of an arithmetic series formula thanks!

Answer : a12 = a1 + 11r (where r is the amount added to each term to get the next). We know 11 of them are added between the first and twelfth. 29 = 11r + 7 r = 2. sum(a1...a12) = sum(a1, a1+r, a1+2r,...,a1+11r) = 12a1 + r sum(1,2,...,11) = 12a1 + r(11*12/2) = 12a1 + 66r = 12*7 + 66*2 = 216 to check, sum = 6(a1+a12) = 6*36 = 216 a1 = 1, r = 7, n = 50 sum = 50*1 + 7 * (49*50/2) = 8625

Question : I'm taking Calc 3 and i cant figure out the difference between a series and sequence. Do they both have sums and tested for convergence?

Answer : A series is the sum of terms in a sequence 1, 2, 3, 4, 5,..... is a sequence 1+2+3+4+5.... is a series