Answer to Question #252825 in Discrete Mathematics for Matheca

Question

(4) Construct a difference table to predict the next term of each sequence.

(a) 9, 4, 3, 12, 37, 84, ...

(b) 10, 10, 12, 16, 22, 30, ..

Answer 1

QUESTION

(4) Construct a difference table to predict the next term of each sequence.

(a) 9, 4, 3, 12, 37, 84, …

ANSWER

(a) Difference table is a table which consists of the differences of the each element with previous the one

9,    4,    3,   12,    37,    84, …   159

  -5     -1    9    25    47      75

     4     10   16    22     28

         6     6    6      6  

1st table: -5, -1, 9, 25, 47, x

2nd table: 4, 10, 16, 22, y

3rd table: 6, 6, 6, 6

From the third table we can assume that y = 22 + 6 = 28

From the second table we can assume that x = 47 + 28 = 75

From the first table we can assume that the next term of the sequence is 84 + 75 = 159

QUESTION

(b) 10, 10, 12, 16, 22, 30, …

ANSWER

10, 10, 12, 16, 22, 30, … 40

0, 2, 4, 6, 8, 10

2, 2, 2, 2, 2

1st difference table: 0, 2, 4, 6, 8, x

2nd difference table: 2, 2, 2, 2, 2

From the second difference table we can assume that x = 8 + 2 = 10

From the first table we can assume that the next term of the sequence is = 10 + 30 = 40