Question

Find an explicit formula for the geometric sequence 96,24,6,1.5

Answer 1

Answer:

Step-by-step explanation:This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by  

1

4

gives the next term. In other words,  

a

n

=

a

1

⋅

r

n

−

1

.

Geometric Sequence:  

r

=

1

4

This is the form of a geometric sequence.

a

n

=

a

1

r

n

−

1

Substitute in the values of  

a

1

=

96

and  

r

=

1

4

.

a

n

=

(

96

)

⋅

(

1

4

)

n

−

1

Simplify the expression.

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a

n

=

96

⋅

1

4

n

−

1

Combine  

96

and  

1

4

n

−

1

.

a

n

=

96

4

n

−

1