t
n
=
a
(
1
5
)
−
Explanation:
Recall that the formula for the
th
of a geometric sequence is:
∣
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
r
−−−−−−−−−−−−−−
where:
term number
first term
common ratio
number of terms
Start by determining the value of
, the first term of the sequence. In your case, that would be
500
.
Use
, and
2
100
to create an equation representing the second term.
Solve for
Now that you have the value of
, you can make a formula representing the
term of the geometric sequence.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
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Answers & Comments
t
n
=
a
(
1
5
)
n
−
1
Explanation:
Recall that the formula for the
n
th
of a geometric sequence is:
∣
∣
∣
∣
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
a
a
t
n
=
a
r
n
−
1
a
a
∣
∣
−−−−−−−−−−−−−−
where:
t
n
=
term number
a
=
first term
r
=
common ratio
n
=
number of terms
Start by determining the value of
a
, the first term of the sequence. In your case, that would be
500
.
Use
a
=
500
, and
t
2
=
100
to create an equation representing the second term.
t
n
=
a
r
n
−
1
100
=
500
r
2
−
1
Solve for
r
.
r
=
1
5
Now that you have the value of
r
, you can make a formula representing the
n
th
term of the geometric sequence.
∣
∣
∣
∣
∣
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
a
a
t
n
=
a
(
1
5
)
n
−
1
a
a