SOLUTION: The 28th term of an AP is -5. Find the common difference if its first term is 31.

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Question 1134391: The 28th term of an AP is -5. Find the common difference if its first term is 31.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The 28th term is the first term plus the common difference 27 times.

31%2B27d+=+-5

Solve for d.

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
There are 27 equal gaps between the 1-st and the 28-th terms,


while the distance between these terms is  31 - (-5) = 36.



Hence, the common difference (the gap between the neighbor terms) is  -36%2F27 = -11%2F3.      ANSWER


CHECK.  a%5B28%5D = a%5B1%5D+%2B+d%2A%2828-1%29 = 31 - 11%2F3.27 = 31 - %284%2F3%29%2A27 = 31 - 36 = -5.    ! Correct !