Answer:
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.
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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
Step-by-step explanation:
Answer: a 180 degree rotation about the origin, then a dilation by a scale factor of 1/3
Step-by-step explanation:
Answer:
(
3
+
1
5
)
(
2
)
(3x+15)(2x)
(3x+15)(2x)
Simplify
1
Distribute
(
3
+
1
5
)
(
2
)
3
(
2
)
+
1
5
(
2
)
Solution
3
(
2
)
+
1
5
(
2
)
Step-by-step explanation:
Answer
33,33 and 22
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Let’s first look at the y-intercept. Since the equation is in y = mx + b form, we know that m is the slope and b is the y-intercept, so the slope is 1/2 and the y-intercept is 2, or (0,2). We can narrow down our search by noticing that C and D don’t intersect (0,2). That leaves A and B.
The slope is calculated by (y_1 - y_2)/(x_1 - x_2) given points (x_1, y_1) and (x_2, y_2). The slope for A is (4-0)/(2-(-2)) = 4/4 = 1 and the slope for B is (2-0)/(0-(-4)) = 2/4 = 1/2. The slope of B matches the slope that we are looking for. So, the answer is B.
