Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
Given:
The first term
�
1
=
729
a
1
=729
The seventh term
�
7
=
1
a
7
=1
We need to find the common ratio
�
r and the intermediate terms
�
2
,
�
3
,
�
4
,
�
5
,
a
2
,a
3
,a
4
,a
5
, and
�
6
a
6
.
The general formula for the
�
n-th term of a geometric sequence is:
�
�
=
�
1
⋅
�
(
�
−
1
)
a
n
=a
1
⋅r
(n−1)
For
�
7
=
1
a
7
=1:
�
7
=
�
1
⋅
�
6
a
7
=a
1
⋅r
6
1
=
729
⋅
�
6
1=729⋅r
6
�
6
=
1
729
r
6
=
729
1
�
=
(
1
729
)
1
6
r=(
729
1
)
6
1
First, we need to calculate
�
r:
�
=
(
1
729
)
1
6
=
72
9
−
1
6
r=(
729
1
)
6
1
=729
−
6
1
Now, let's compute
�
r:
729
=
3
6
729=3
6
72
9
−
1
6
=
(
3
6
)
−
1
6
=
3
−
1
=
1
3
729
−
6
1
=(3
6
)
−
6
1
=3
−1
=
3
1
So,
�
=
1
3
r=
3
1
.
Now, we can find the intermediate terms:
�
2
=
�
1
⋅
�
=
729
⋅
1
3
=
243
a
2
=a
1
⋅r=729⋅
3
1
=243
�
3
=
�
1
⋅
�
2
=
729
⋅
(
1
3
)
2
=
729
⋅
1
9
=
81
a
3
=a
1
⋅r
2
=729⋅(
3
1
)
2
=729⋅
9
1
=81
�
4
=
�
1
⋅
�
3
=
729
⋅
(
1
3
)
3
=
729
⋅
1
27
=
27
a
4
=a
1
⋅r
3
=729⋅(
3
1
)
3
=729⋅
27
1
=27
�
5
=
�
1
⋅
�
4
=
729
⋅
(
1
3
)
4
=
729
⋅
1
81
=
9
a
5
=a
1
⋅r
4
=729⋅(
3
1
)
4
=729⋅
81
1
=9
�
6
=
�
1
⋅
�
5
=
729
⋅
(
1
3
)
5
=
729
⋅
1
243
=
3
a
6
=a
1
⋅r
5
=729⋅(
3
1
)
5
=729⋅
243
1
=3
Thus, the 5 geometric means between 729 and 1 are:
243
,
81
,
27
,
9
,
3
243,81,27,9,3
Step-by-step explanation:
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
