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#