How do you find an for the arithmetic series $S_16=856$ and $a_1=76$ ?

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Answer 1 · 2016-02-06T23:37:49

Well the sum of an arithmetic series is given by

$S_n=n/2*(a_1+a_n)$

Now hence $S_16=856$ and $a_1=76$

we have that

$856=16/2*(76+a_16)=>a_16=107-76=>a_16=31$

and $a_n=a_1+(n-1)*r=>a_16=a_1+15*r=> r=(a_16-a_1)/15=>r=(31-76)/15=>r=-3$

So it is an arithemtic progression with first term $a_1=76$
and ratio $r=-3$

How do you find an for the arithmetic series S_16=856S_16=856 and a_1=76a_1=76?