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 October 14th, 2018, 05:21 AM #1 Newbie   Joined: Oct 2018 From: arizona Posts: 6 Thanks: 0 How Can I Represent These Progressions in Sigma Notation? I would like to represent the following finite progressions in sigma notation: 1. Finding the $n^\text{th}$ term of a geometric progression: $a_n=a_1(r^{n-1})$, where $a_1$ is the first time and $r$ is the common ratio 2. The sum of a geometric progression: $S_n=a_1\frac{1-r^n}{1-r}$ 3. Determining the $n^\text{th}$ term of an arithmetic progression: $a_n=a_1+(n-1)d$, where $d$ is the common difference 4. And finally, the sum of an arithmetic progression: $S_n=\frac{n}{2}(2a_1+(n-1)d)$ Last edited by skipjack; October 14th, 2018 at 06:37 AM. October 14th, 2018, 06:39 AM #2 Global Moderator   Joined: Dec 2006 Posts: 21,105 Thanks: 2324 Sigma notation isn't needed for the first and third parts of the question. 2. $\displaystyle (1 - r)S_n = \sum_{k=1}^n a_1*r^{k-1} - \sum_{k=1}^n a_1*r^{k} = \sum_{k=1}^n a_1*r^{k-1} - \sum_{k=2}^{n+1} a_1*r^{k-1} = a_1- a_1r^n$ $\displaystyle \therefore S_n = a_1\frac{1 - r^n}{1 - r}$ 4. $\displaystyle 2S_n = \sum_{k=1}^n (a_1 + (k - 1)d) + \sum_{k=1}^n (a_1 + (n - k)d) = \sum_{k=1}^n (2a_1 + (n - 1)d) = n(2a_1 + (n - 1)d)$ $\displaystyle \therefore S_n = {\small\frac{n}{2}}(2a_1 + (n - 1)d)$ Tags arithmetic progression, geometric sequence, notation, progression or series, progressions, represent, sigma, summation, summations Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Shamieh Calculus 2 November 4th, 2013 08:08 PM Shamieh Calculus 2 November 4th, 2013 07:09 PM Shamieh Calculus 1 November 4th, 2013 05:29 PM calebh Calculus 2 November 26th, 2012 07:50 AM daemonlies Algebra 8 April 28th, 2011 10:13 PM

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