<span>A1 is the 1st term r is the difference, they can say "r" or "d" for the difference 1st a1 is the first term = -3 2nd "r" is the difference between each consecutive terms (coming after each other) = 1.5 the rule to get any term of the sequence as we add 1.5 each time is --> a1+(n-1)*d a1 --> 1st term , n --> order of the term u want whether 2nd, 3rd , 25th d --> difference so to get the 2nd--> -3+(2-1)*1.5= -1.5 to get the 3rd --> -3 +(3-1)*1.5 = 0 and so on</span>
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:
Plz help will make the Brainly
Step-by-step explanation:
Answer:
(x - 12)²/9
Step-by-step explanation:
y = 3sqr(x) + 12
Make x the subject:
y - 12 = 3sqrt(x)
(y - 12)/3 = sqrt(x)
Square both sides
(y - 12)²/9 = x
Interswitch variables
inverse function is:
(x - 12)²/9
If f(x) = (x + 12)^⅓
Then,
y = (x + 12)⅓
y³ = x + 12
y³ - 12 = x
f inverse:
x³ - 12
