SOLUTION: I am trying to help my daughter do her homework. It has been many years since I graduated from HS. In fact many many many and then some. I know I am going to have to pick the bo

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Question 92543This question is from textbook Holt, Rinehart and Wilson
: I am trying to help my daughter do her homework. It has been many years since I graduated from HS. In fact many many many and then some. I know I am going to have to pick the books back up. Here is my question:
The third and fourth terms of a sequence are 26 and 40. If the second differences are a constant 4, what are the first five terms of the sequence?
This question is from textbook Holt, Rinehart and Wilson

Found 2 solutions by CubeyThePenguin, greenestamps:
Answer by CubeyThePenguin(3113)   (Show Source): You can put this solution on YOUR website!
(numbers in parentheses were filled in due to context)

10, 16, 26, 40
difference: (6),(10), 14
second diff: 4, 4


first 5 terms: 10, 16, 26, 40, 58

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


As is often the case, the response from tutor @CubeyThePenguin does nothing to help you and your daughter learn how to solve the problem....

Here is what we have....

   ___   ___   26    40    ___   the 3rd and 4th terms are 26 and 40
      ___   ___   14    ___      The only thing we know about the first differences is that one of them is 14
          4     4     4          we know the second differences are a constant 4

You can use the constant second differences to work both forward and backward in the sequence to determine the first differences (the successive first differences have a constant difference of 4)...

   ___   ___   26    40    ___
        6    10   14    18
          4     4     4

And finally you can similarly use those first differences to determine the original sequence.

    10    16   26    40    58
        6    10   14    18
          4     4     4


ANSWER: The first five terms of the original sequence are 10, 16, 26, 40, and 58.


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