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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