SOLUTION: Find the arithmetic series whose 6th term is 0 and whose 10th term is 16. Show that there must be 14 terms in the series if its sum is 84.

Algebra ->  Sequences-and-series -> SOLUTION: Find the arithmetic series whose 6th term is 0 and whose 10th term is 16. Show that there must be 14 terms in the series if its sum is 84.       Log On


   

Question 1175457: Find the arithmetic series whose 6th term is 0 and whose 10th term is 16. Show that there must be 14 terms in the series if its sum is 84.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
 a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad
a%5B6%5D=a%5B1%5D%2B%285%29%2Ad = 0  
a%5B10%5D=a%5B1%5D%2B%289%29%2Ad = 16 
   a + 9d = 16 
   a + 5d = 0    |Subtract 2nd from 1st
       4d = 16
        d = 4   and a1 = -20    +a%5B1%5D+=+-5d
   
S%5Bn%5D=%28n%28a%5B1%5D%2Ba%5Bn%5D%29%29%2F2   a%5B14%5D=-20+%2B%2813%29%2A4  
S%5B14%5D=%2814%28-20+%2B+32%29%29%2F2+=+84
Wish You the Best in your Studies.