SOLUTION: given a1=28 an=-77 and sn =-196 in an A.P find the 10th term and the sum of the first 10 terms

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Question 1072952: given a1=28 an=-77 and sn =-196 in an A.P find the
10th term and the sum of the first 10 terms
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
                <--first term
   <--formula for nth term




  <-- formula for nth term

 Substitute for a1 and (n-1)d=-105







Multiply through by 2





          <--number of terms whose sum is -77

We'll need d, so




        <-- common difference, d

To find 10th term:



Substitute n=10, a1 = 28, n=10, d=-15







     <-- 10th term

 <-- formula for sum of first n terms











Checking, the sequence is:

28,13,-2,-17,-32,-47,-62,-77,-92,-107

Add them

28+13-2-17-32-47-62-77-92-107 = -395

Add the first 8 terms

28+13-2-17-32-47-62-77 = -196

Everything checks.

Edwin
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