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Find the 8th term of the geometric sequence –4, 12, –36, 108, –324,

Sagot :

Answer:

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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

3

gives the next term. In other words,

a

n

=

a

1

⋅

r

n

−

1

.

Geometric Sequence:

r

=

3

This is the form of a geometric sequence.

a

n

=

a

1

r

n

−

1

Substitute in the values of

a

1

=

4

and

r

=

3

.

a

n

=

(

4

)

⋅

(

3

)

n

−

1

Remove parentheses.

a

n

=

4

⋅

3

n

−

1

Substitute in the value of

n

to find the

n

th term.

a

8

=

4

⋅

3

(

8

)

−

1

Subtract

1

from

8

.

a

8

=

4

⋅

3

7

Raise

3

to the power of

7

.

a

8

=

4

⋅

2187

Multiply

4

by

2187

.

a

8

=

8748

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