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:
Restudy and try to take it again.
Step-by-step explanation:
Try watching math videos and do extra studying on the areas you missed on your last attempt.
Each two digit number has two numbers (duh!). Let's allow the tens digit to be x and the units digit to be y. Tens digit is 3 less than the units digit: x = y-3 Original number is 6 more than 4 times the sum of the digits: 10x+y-6 = 4x + 4y This gives us simultaneous equations!First let's clear the mess: 1. x= y-32. 6x-3y=6 Substitute 1 into 2: 6(y-3) -3y =66y - 18 - 3y = 6
3y = 24y = 8 Our units digit is 8 Substitute y= 8 into 1. x = y - 3x = 5 Our tens digit is 5 Therefore, our number is 58
Answer:
D. - 1/6
Step-by-step explanation:
M + 2/3 = 1/2
M = 1/2 - 2/3
