Question 1151999

The series which we want to add can be given as :


{{{-24}}},{{{-22}}},{{{-20}}},........,{{{224}}},{{{226}}}


Sum of N numbers in AP is given by:


{{{S[n]=n(a+l)/2}}} ........where, {{{a}}} = First element in AP,{{{ l}}} = Last element in AP


According to the series we have number of total elements {{{n }}}which can be calculated as:


{{{l=a+(n-1)d}}}, where {{{n}}} = number of elements.


in your case {{{l=226}}}, {{{a=-24}}},{{{d=2}}}


{{{l=a+(n-1)d}}}

{{{226=-24+(n-1)2}}}

{{{226+24=(n-1)2}}}

{{{250/2=n-1}}}

{{{125=n-1}}}

{{{125+1=n}}}

{{{n=126}}}


now we can find the sum:

{{{S[n]=n(a+l)/2}}}.....substitute {{{n}}},{{{a}}}, and {{{l}}}

{{{S[126]=126(-24+226)/2}}}

{{{S[126]=126(202)/2}}}

{{{S[126]=12726}}}