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If I have a sequence - lets say an algebraic sequence 

and a function - really doesn't matter what function as long as it takes some sort of arguments

 

sequence : [1,3,5,7,9,...]

function : result = x*7 + x - 3 

 

what I am interested in is the following sequence : [result @ 1, result @ 3, result @ 5,result @ 7,result @ 9, ...]

 

What would the formula be for the sum of the above values

 Mar 9, 2021
 #1
avatar+32019 
+1

Deleted. Misinterpreted the question!

 Mar 9, 2021
edited by Alan  Mar 9, 2021
 #3
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my bad for the lacking explanation
I'm bad with words so I'll give an example

 

say we have the following sequence : 
    π‘Žπ‘›=1+(π‘›βˆ’1)*2
    thus π‘Žπ‘›=2*𝑛-1

 

and the following function : 
    X𝑛 = π‘Žπ‘›^2 + 12 * π‘Žπ‘› + 7
    thus X𝑛 = 4*𝑛^2 + 20*𝑛 - 4

 

how do I get the sum of say the first 10 terms :
    sum Xn from n = 1 to n = 10

Guest Mar 9, 2021
 #2
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my bad for the lacking explanation
I'm bad with words so I'll give an example

 

say we have the following sequence : 
    π‘Žπ‘›=1+(π‘›βˆ’1)*2
    thus π‘Žπ‘›=2*𝑛-1

 

and the following function : 
    X𝑛 = π‘Žπ‘›^2 + 12 * π‘Žπ‘› + 7
    thus X𝑛 = 4*𝑛^2 + 20*𝑛 - 4

 

how do I get the sum of say the first 10 terms :
    sum Xn from n = 1 to n = 10

 Mar 9, 2021
 #4
avatar+32019 
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Apologies, I misread your question! 

 

Unfortunately, there is no general rule for arbitrary functions.  For some functions you can find an expression for the sum, for others you can't.  Do you have some specific functions in mind?

Alan  Mar 9, 2021
 #5
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not really I'm trying to cast a line in 3d space and then summate the the values starting from one point along the line until I reach a saturation value

Guest Mar 9, 2021
 #6
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noted that said values are specific to the space transversed which is determined by other functions

Guest Mar 9, 2021

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