Question

Chairs for an orchestra are positioned in a curved form with the conductor at the center. The front row has 16 chairs, the second has 20 and the third has 24, and so on. a. Write a recursive rule for this sequence: _______________________________ a. Write a explicit rule for this sequence: _______________________________

Answer 1

(a) The recursive rule of the sequence is

`a_n=a_(n-1)+4`

(b) The explicit rule for this sequence is

`a_n=16+(n-1)4`

Explanation:

Given that,

The front row has 16 chair.

The second row has 20 chairs.

The third row has 24 chairs.

The difference of chairs of first row to second row is =(20-16)

=4

The difference of chairs of second row to third row is =(24-20)

=4

The difference of chairs remains same. So given sequence is a arithmetic sequence.

We know ,

The nth term of arithmetic sequence is represented by

`a_n=a+(n-1)d`

a=first term of the sequence

d= common difference.

and

`a_n=a_(n-1)+d`

Here a= the number of chairs in first row = 16

d=4

The recursive rule of the sequence is

`a_n=a_(n-1)+4`

(b)

Row 1: 16

Row 2: 16+4------------------- 16+(2-1)4 =16+1.4

Row 3: 16+4+4-----------------16+(3-1)4=16+2.4

Row 4:16+4+4+4---------------16+(4-1)4=16+3.4

The explicit rule for this sequence is

`a_n=16+(n-1)4`