Question 694434

Hello I had a question regarding arithmetic sequences. 
Here we have 1+3+5+...+915.
How would I find the sum using a formula?
Thank You all for your time to help and teach. 


This problem can be solved by using the number of numbers formula: {{{n = (a[n] - a[1])/2 + 1}}}, first, to determine the number of numbers, or "n," with {{{a[1]}}} being the first term, and = 1, and {{{a[n]}}} being the last term, and = 915.


{{{n = (915 - 1)/2 + 1}}} ----- {{{n = (914/2) + 1}}} ----- {{{n = 457 + 1}}} ----- {{{n = 458}}}



The formula for sum of an arithmetic sequence, or A.P. is: {{{S[n] = (n/2)(2a[1] + (n - 1)d)}}}, with {{{S[n] = S[458]}}}, 1st term, or {{{a[1]}}} = 1; n, or amount of terms to be summed = 458, and d, or common difference = 2
 

Therefore, {{{S[n] = (n/2)(2a[1] + (n - 1)d)}}} becomes: {{{S[458] = (458/2)(2(1) + (458 - 1)2)}}}


{{{S[458] = 229(2 + (457)2)}}}


{{{S[458] = 229(2 + 914)}}}


{{{S[458] = 229(916)}}}


{{{S[458]}}}, or sum of the 458 terms in the series = {{{highlight_green(209764)}}}


You can do the check!!


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