Question

> Construct a difference table to predict the next term of each sequence.

a) -1, 4, 21, 56, 115, 204, …

b) 9, 4, 3, 12, 37, 84, …

> Write the first twenty positive terms of the Fibonacci sequence.

Answer 1

Given :

a) -1, 4, 21, 56, 115, 204, …

b) 9, 4, 3, 12, 37, 84, …

To Find : Construct a difference table to predict the next term of each sequence.

first twenty positive terms of the Fibonacci sequence.

Solution:

-1,       4,       21,     56,     115,      204, …     329    

   5        17      35       59      89           125        

      12       18       24      30          36            

            6          8         6          6

So next term is 329

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

     -5          -1         9         25        47            75          

           4          10       16         22         28                  

                6          6         6           6  

so next term is 159

Fibonacci sequence.

a₁ = 1

a₂ = 1

aₙ =  aₙ₋₁   + aₙ₋₂

first twenty positive terms of the Fibonacci sequence.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 , 987 , 1597 , 2584 , 4181 , 6765

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