Question 1128108
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2-nd term = -3 = 1 - 4 = {{{1 - 2^2}}}

3-rd term = 6 = -3 + 9 = {{{-3 + 3^2}}}

4-th term = -10 = 6 - 16 = {{{6 - 4^2}}}

5-th term = 15 = -10 + 25 = {{{-10 + 5^2}}}.


The pattern is this recurrent formula  {{{a[n+1]}}} = {{{a[n] + (-1)^n*(n+1)^2}}}.


To find  {{{a[100]}}},  take  n+1 = 100 (hence n = 99)  and  {{{a[99]}}} = 4950  (as it is given).


Then you will get


{{{a[100]}}} = {{{4950 + (-1)^99*(99+1)^2}}} = {{{4950 + (-1)*100^2}}} = 4950 - 10000 = -5050.     <U>ANSWER</U>  
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My understanding is that not only an answer does matter - the solution (I mean the correct and correctly presented solution) does matter, too.


It is why I wrote this post after the post by @Mtrkcrc.