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    I know this is an easy question but once you've overanalysed something its hard to go back !
    The sum of the first n numbers is sn = n/2 (2a+(n-1)d) or sn= n/2 (a+l)
    And the sum of the first n whole numbers is sn= n/2 n(n+1)

    My question is, what differs between these two formulas? When do you use each one? Why does the sum of n whole numbers need a different formula?
    Again, an easy stupid question but its the last question I have on this chapter after really struggling with sequences and series so thanks <3
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    (Original post by AmbaJade)
    I know this is an easy question but once you've overanalysed something its hard to go back !
    The sum of the first n numbers is sn = n/2 (2a+(n-1)d) or sn= n/2 (a+l)
    And the sum of the first n whole numbers is sn= n/2 n(n+1)

    My question is, what differs between these two formulas? When do you use each one? Why does the sum of n whole numbers need a different formula?
    Again, an easy stupid question but its the last question I have on this chapter after really struggling with sequences and series so thanks <3
    sn= n/2 n(n+1) cannot be right... try putting 4 for n... the answer should be 10...
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    (Original post by AmbaJade)
    I know this is an easy question but once you've overanalysed something its hard to go back !
    The sum of the first n numbers is sn = n/2 (2a+(n-1)d) or sn= n/2 (a+l)
    And the sum of the first n whole numbers is sn= n/2 n(n+1)

    My question is, what differs between these two formulas? When do you use each one? Why does the sum of n whole numbers need a different formula?
    Again, an easy stupid question but its the last question I have on this chapter after really struggling with sequences and series so thanks <3
    S_n = \frac{n}{2} (2a+(n-1)d) and S_n= \frac{n}{2}(a+l) are for arithmetic sequences with common difference d.

    Whereas, S_n= \frac{n}{2}(n+1) is for the sequence 1,2,3...,n i.e. an arithmetic sequence with first term 1 and common difference 1.

    So if you set a=1 and d=1 into the first formula, you will get S_n= \frac{n}{2}n(n+1). Likewise, a=1 and l=n in the second formula will yield the same result.
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    The formula for the sum of the first n natural numbers is a special case of the general sum of an arithmetic series where you just add consecutive natural numbers up to n.
 
 
 
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