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
8.4617....
Hope this helped you :)
The correct answer is A. 10 bracelets
It’s a triangle
s
r t
rs= 2x+10 and st= x-4
the sides are equal so equal them together then solve
2x+10=x-4
+ 4 +4
2x+14=x
you got x alone so x=2x+14
now you plug in 2x+14 in for the x in rs and st
rs= 2(2x+14)+10
4x+28+10
4x+38
st= (2x+14)-4
2x+14-4
2x-10
