SOLUTION: Construct a difference table to predict the next term of the sequence.
3, −2, 0, 15, 49, 108, . . .
Algebra.Com
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
RELATED QUESTIONS
Construct a difference table to predict the next term of the sequence... (answered by greenestamps)
Construct a difference table to predict the next term of the sequence.
−1, 3, 22, 61,... (answered by Boreal,greenestamps)
In exercises 1-6, construct a difference table to predict the next term of each sequence. (answered by RAY100)
1. Find the 20th term of the following sequence.
-6, -4, -2, 0, ...
32
44
46
2.... (answered by ewatrrr)
Describe a pattern in the sequence of numbers. Predict the next number.
1) 1, 2, 6,... (answered by sudhanshu_kmr,Edwin McCravy)
Solve cos x − 1 = 0 on the interval 0 ≤x ≤ π/2.
Describe the... (answered by stanbon)
Solve the following problems completely and logically.
Problem 1: Construct a... (answered by greenestamps)
Use inductive reasoning to predict the next number in each sequence.
3, 7, 11, 15,... (answered by stanbon,yannick,scott8148,Edwin McCravy)
1. Describe a pattern in each sequence. What are the next two terms of each sequence?
(answered by KMST)