SOLUTION: the first term of an arithmetic sequence is -14 while the sum of the first 20 term is 860. find the 20th term.

Question 800964: the first term of an arithmetic sequence is -14 while the sum of the first 20 term is 860. find the 20th term.
Answer by Finavon(81) (Show Source): You can put this solution on YOUR website!
Let x = difference between terms and Sum(n) = sum of 1st n terms
Series is -14, (-14+x), (-14+2x), (-14+3x), ... (-14+(n-1)*x)
Sum(n) = -14 + (-14+x) + (-14+2x) + (-14+3x) + ... + (-14+(n-1)*x)
Rearrange Sum(n) = (-14)*n + x*(1+2+3+ .. +(n-1))
Add 2nd arithmetic series (reversed)
Sum(n) = -14*n + x*( (1+2+3+ .. +(n-1)) + ((n-1)+(n-2)+(n-3)+ .. +1) )/2
=-14*n + x*n*(n-1)/2
So Sum(20)=-14*20+ x*20*(20-1)/2 = -280+x*20*19/2
So 860=-280+190*x

20th term is -14+19*6=114-14=100
20th term is 100
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