Question 353570: The third and fourth terms of a sequnce are 26 and 40. If the second differences are a constant 4, what are the first five terms of the sequence
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! The third and fourth terms of a sequnce are 26 and 40. If the second differences are a constant 4, what are the first five terms of the sequence
We have this information. Put blanks for the unknown values:
n an 1st diffs 2nd diffs
1 __
__
2 __ 4
__
3 26 4
__
4 40 4
__
5 __
Since we have two consecutive terms, the 3rd and 4th,
we can find the first difference between them by subtracting
26 from 40, getting 14, so we fill that in
n an 1st diffs 2nd diffs
1 __
__
2 __ 4
__
3 26 4
14
4 40 4
__
5 __
We can fill in the 2nd first difference by adding 4 to 14 getting 18:
n an 1st diffs 2nd diffs
1 __
__
2 8 4
18
3 26 4
14
4 40 4
__
5 __
We can fill in the 1st first difference by adding 4 to 18 getting 22:
n an 1st diffs 2nd diffs
1 __
22
2 __ 4
18
3 26 4
14
4 40 4
__
5 __
We can fill in the last 1st difference by subtracting 4 from 14 getting 10:
n an 1st diffs 2nd diffs
1 __
22
2 __ 4
18
3 26 4
14
4 40 4
10
5 __
We can fill in a5 by adding 10 to 40 getting 50:
n an 1st diffs 2nd diffs
1 __
22
2 __ 4
18
3 26 4
14
4 40 4
10
5 50
We can fill in a2 by subtracting 18 from 26 getting 8:
n an 1st diffs 2nd diffs
1 __
22
2 8 4
18
3 26 4
14
4 40 4
10
5 50
Finally we can fill in a1 by subtracting 22 from 8 getting -14:
n an 1st diffs 2nd diffs
1 -14
22
2 8 4
18
3 26 4
14
4 40 4
10
5 50
So the first 5 terms of the sequence are
a1=-14, a2=8, a3=26, a4=40, a5=50.
Later on you'll have to find the general term, which is
an = -2nē+28n-40
Edwin
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