Question

Write a rule for the n th term of the sequence for which az = 4 and r= 2.
=

Answer 1

Explanation:

The general form for a geometric sequence is:

a

n

=

a

1

⋅

r

n

−

1

With this, you can write a system of equations:

a

2

=

a

1

⋅

r

2

−

1

a

5

=

a

1

⋅

r

5

−

1

2

=

a

1

⋅

r

1

0.25

=

a

1

⋅

r

4

r

4

r

1

=

0.25

2

r

3

=

0.125

r

=

0.5

Now, find the first term.

a

2

=

a

1

⋅

0.5

1

2

=

a

1

⋅

0.5

a

1

=

4

Using the formula stated above, we get:

a

n

=

4

⋅

0.5

n

−

1