5,-15,45,-135,? what is the next number

405 ...

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

=

5

and

r

=

3

.

a

n

=

(

5

)

⋅

(

3

)

n

-

1

Remove parentheses.

a

n

=

5

⋅

3

n

-

1