Question 708337: Construct a difference table to predict the next term of the sequence.
3, −2, 0, 15, 49, 108, . . .
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Too late probably, but here's what I would do.
I would put those numbers in a column, like this:
3
-2
0
15
49
108
I would make a second column with the differences.
subtract the first number from the second, the second number from the third, and so on.
-2-3=-5
0-(-2)=2
15-0=15
49-15=34
108-49=59
Since I see no pattern in those differences,
I would make a third column with the differences of those differences:
2-(-5)=7
15-2=13
34-15=19
59-34=25
Then I would calculate differences of differences of differences for a fourth column:
13-7=6
19-13=6
25-19=6
It could look like this:
...3...-5....7...6
..-2....2...13...6
...0...15...19...6
..15...34...25
..49...59
.108
Finally, I see a pattern.
All the numbers in the fourth column are 6. there would be more 6's if we continue the pattern.
The numbers on the third column were increasing by 6 as they went down.
The number after 25 would have been 25+6=31.
The numbers in the second column increased by adding the number from the third column.
-5+7=2
2+15=15
15+19=34
34+25=59
That means that the number after 59 would be 59+31=90.
the numbers in the first column were calculated the same way using the second column:
15+34=49
49+59=108
What comes next is
108+90=198
The next number in the sequence is  .
The table would be extended like this:
...3...-5....7...6
..-2....2...13...6
...0...15...19...6
..15...34...25...6
..49...59...31...6
.108...90...37
.198..127
.325
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