Question 110183
First notice that the sign on each term alternates and the odd numbered terms are negative.  That means a good place to start is to have each term contain the factor {{{(-1)^n}}}, which yields a positive 1 for all even n, and a negative 1 for all odd n.
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The next thing to notice is that the absolute value of each element increases by 5 each subsequent element, so 5n is a good expression for that.
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Putting it all together you get:
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{{{(-1)^n*5n}}}
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Check:
{{{(-1)^1*5*1=(-1)*5=-5}}}
{{{(-1)^2*5*2=1*5*2=10}}}
{{{(-1)^3*5*3=(-1)*5*3=-15}}}
{{{(-1)^4*5*4=5*4=20}}}
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And the 5th term should be:
{{{(-1)^5*5*5=(-1)*5*5=-25}}}
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Exercise for the student:  What would you do if your series had the odd terms positive and the even terms negative, i.e. the exact opposite of the problem given?