SOLUTION: how to find T1 (first term) in sequence or series when T1 isnt given but say t2 and t4 is or something related to that

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Question 825921: how to find T1 (first term) in sequence or series when T1 isnt given but say t2 and t4 is or something related to that
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
The answer depends on what type of sequence it is.

If it is an arithmetic sequence then...
  1. Subtract the two terms you know. For example, if the 2nd term was 12 and the 4th term was 18 subtract 18 and 12 (which is 6).
  2. Divide the difference by the difference in the term numbers. This will give you the common difference, "d", for the arithmetic sequence. In the example above, the difference in the terms is 2 (4-2) so we divide the 6 (from step 1) by 2 to get 3.
  3. Work backward from the lowestest number term. Subtract the result of the division (n-1) times (where "n" is the number of the lowest numbered term). In the example, n would be 2 so n-1 would be 1. So we subtract the result of the division 1 time from 12 giving us 9. This is the first term of the sequence.
If the sequence is a geometric sequence then...
  1. Divide the two terms: The later term divided by the earlier term (not necessarily the larger term divided by the smaller term). Using the example from above, we would divide 18 by 12 getting 3/2.
  2. Subtract the term numbers. Again with the example, this would be 4-2 or 2.
  3. Find a root of the number from step one. The type of root is the number from step 2. This result will be the common ratio, "r", of the sequence. With our example, we would find a 2nd (better known as a square) root of 3/2: .
  4. Work backward from the lowest numbered term. Divide by the result in step 4, "r", n-1 times (with "n" being the number of the lowest number term. This will be the first term. With our example we would divide 12, the second term, 2-1 or 1 time by :

    (Note: Most geometric sequences have simpler numbers for "r".)
If the sequence is neither arithmetic nor geometric, then I can't help you without knowing more about the sequence.
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