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
2
3
2
3
gives the next term. In other words,
a
n
=
a
1
⋅
r
n
−
1
a
n
=
a
1
⋅
r
n
-
1
.
Geometric Sequence:
r
=
2
3
r
=
2
3
This is the form of a geometric sequence.
a
n
=
a
1
r
n
−
1
a
n
=
a
1
r
n
-
1
Substitute in the values of
a
1
=
1
2
a
1
=
1
2
and
r
=
2
3
r
=
2
3
.
a
n
=
(
1
2
)
⋅
(
2
3
)
n
−
1
a
n
=
(
1
2
)
⋅
(
2
3
)
n
-
1
Apply the product rule to
2
3
2
3
.
a
n
=
1
2
⋅
2
n
−
1
3
n
−
1
a
n
=
1
2
⋅
2
n
-
1
3
n
-
1
Multiply
1
2
1
2
and
2
n
−
1
3
n
−
1
2
n
-
1
3
n
-
1
.
a
n
=
2
n
−
1
2
⋅
3
n
−
1
a
n
=
2
n
-
1
2
⋅
3
n
-
1
Cancel the common factor of
2
n
−
1
2
n
-
1
and
2
2
.
Tap for more steps...
a
n
=
2
n
−
2
3
n
−
1
a
n
=
2
n
-
2
3
n
-
1
Substitute in the value of
n
n
to find the
n
n
th term.
a
5
=
2
(
5
)
−
2
3
(
5
)
−
1
a
5
=
2
(
5
)
-
2
3
(
5
)
-
1
Simplify the numerator.
Tap for more steps...
a
5
=
8
3
(
5
)
−
1
a
5
=
8
3
(
5
)
-
1
Simplify the denominator.
Tap for more steps...
a
5
=
8
81
a
5
=
8
81
Answer: Answer in the photo
Step-by-step explanation:
I believe the answer is b= -5
When comparing, think of the signs as a crocodile. A crocodile will want to eat greater (bigger) numbers than smaller numbers. So, you can think of it as that way.
2. 0.5 < 0.8 ... 0.8 is greater than 0.5
5. 0.7 = 0.70 ... This is same. 0.70 just has an extra 0 which you don't need.
8. 2.9 > 2.8 ... 2.9 is greater since 9 is bigger than 8.
11. 0.65 > 0.36 ... 65 is greater than 36. Therefore, 0.65 is greater.
14. 4.50 > 4.05 ... 4.50 has a five in the tenth place. 4.05 has five in the hundredth place.
17. 6.01 < 6.1 ... 6.1 has a one in the tenth place. 6.01 has a one in the hundredth place.
The answer is B for the first part, and I think the solution is (6,7).
