SOLUTION: please help me to make n the subject of the formula in: Sn= n/2{2a+(n-1)d}

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Question 1127295: please help me to make n the subject of the formula in: Sn= n/2{2a+(n-1)d}
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
----------(does not render properly using the subscript)...
(dropping subscript also for convenience)

S=%28n%2F2%29%282a%2B%28n-1%29d%29



S=%28n%2F2%29%282a%2B%28n-1%29d%29

%282%2Fn%29S=2a%2B%28n-1%29d

%282%2Fn%29S=2a-dn-d

n%282%2Fn%29S=2an-dn%5E2-dn

2S=-dn%5E2-dn%2B2an

dn%5E2%2Bdn-2an%2B2S=0

dn%5E2%2B%28d-2a%29n%2B2S=0
-

n=%282a-d%2B-+sqrt%28%28d-2a%29%5E2-4d%2A2S%29%29%2F%282d%29

highlight%28n=%282a-d%2B-+sqrt%28%28d-2a%29%5E2-8dS%29%29%2F%282d%29%29