SOLUTION: If the 4th term of an arithmetic sequence is 31 and the 8th term of the sequence is 59, find the 1st term of the sequence.

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Question 822434: If the 4th term of an arithmetic sequence is 31 and the 8th term of the sequence is 59, find the 1st term of the sequence.
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi,

If the 4th term of an arithmetic sequence is 31 and the 8th term of the sequence is 59, find the 1st term of the sequence. 

a%5Bn%5D+=+a%5B1%5D+%2B%28n-1%29d

a%5B4%5D+=+a%5B1%5D+%2B3d+=+31

a%5B8%5D+=+a%5B1%5D+%2B7d+=+59

 a1 + 7d = 59 

 a1 + 3d = 31    |subtracting 2nd EQ from 1st

     4d = 28

      d = 7    and a%5B1%5D+=+highlight_green%2810%29    (a1 = 59-49)

 CHECKING our answer***

a%5B4%5D+=+10+%2B+21+=+31