
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: $a_n=a_1(r^{n1})$, where $a_1$ is the first time and $r$ is the common ratio 2. The sum of a geometric progression: $S_n=a_1\frac{1r^n}{1r}$ 3. Determining the $n^\text{th}$ term of an arithmetic progression: $a_n=a_1+(n1)d$, where $d$ is the common difference 4. And finally, the sum of an arithmetic progression: $S_n=\frac{n}{2}(2a_1+(n1)d)$ Last edited by skipjack; October 14th, 2018 at 06:37 AM. 
October 14th, 2018, 06:39 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,089 Thanks: 1902 
Sigma notation isn't needed for the first and third parts of the question. 2. $\displaystyle (1  r)S_n = \sum_{k=1}^n a_1*r^{k1}  \sum_{k=1}^n a_1*r^{k} = \sum_{k=1}^n a_1*r^{k1}  \sum_{k=2}^{n+1} a_1*r^{k1} = a_1 a_1r^n$ $\displaystyle \therefore S_n = a_1\frac{1  r^n}{1  r}$ 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  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Write the sum in sigma notation(3)  Shamieh  Calculus  2  November 4th, 2013 08:08 PM 
Write the sum in sigma notation(2)  Shamieh  Calculus  2  November 4th, 2013 07:09 PM 
Write the sum in sigma notation  Shamieh  Calculus  1  November 4th, 2013 05:29 PM 
Sigma Notation  calebh  Calculus  2  November 26th, 2012 07:50 AM 
Sigma Notation  daemonlies  Algebra  8  April 28th, 2011 10:13 PM 