IXL - Write a formula for a geometric sequence (Algebra 2 practice)

or

Write
an
equation
to
describe
the
sequence
below.
Use
n
to
represent
the
position
of
a
term
in
the
sequence,
where
n = 1
for
the
first
term.

1

,

3

,

9

,

...

Write your answer using decimals and integers.

an = ()n - 1

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or

Learn with an example

question

Write
an
equation
to
describe
the
sequence
below.
Use
n
to
represent
the
position
of
a
term
in
the
sequence,
where
n = 1
for
the
first
term.

9

,

18

,

36

,

...

Write your answer using decimals and integers.

an = ()n - 1

key idea

The
formula
for
the
n^th
term
of
a
geometric
sequence
is

an = a1(r)^{n - 1}

where
an
is
the
n^th
term,
a1
is
the
first
term,
r
is
the
common
ratio,
and
n
is
the
position
of
a
term
in
the
sequence.

solution

First
find
a1
,
the
first
term
in
the
sequence.

9

,

18

,

36

,

...

The
first
term,
a1
,
is
9
.

Next
find
r
,
the
common
ratio
between
consecutive
terms.

9

,

18

,

36

,

...

× 2

× 2

The
common
ratio,
r
,
is
2
.

Finally,
plug
a1
=
9
and
r
=
2
into
the
formula.

an = a1(r)^{n − 1}

an = 9(2)^{n − 1}

The
sequence
9 , 18 , 36 , ...
is
described
by
the
equation
an = 9(2)^{n − 1}
.

Looking for more? Try these:

Lesson: Geometric sequences

or

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MM.2Find terms of a geometric sequence

Lesson: Geometric sequences