6. The first term of a geometric sequence is 8, and the second term is 4. Find the fifth term. *
a.1/2
b.1/4
c.1/6
d.18
7. The first term of a geometric sequence is 3, and the third term is 4/3. Find the fifth term. *
a.2
b.8/9
c.16/27
d.5
Answers
Answer:6. a GPis of the form
a
,
a
r
,
a
r
2
,
a
r
3
,
...
,
a
r
n
−
1
...
...
.
we are given
a
=
8
a
r
=
4
we have to find the fifth term
r
=
a
r
a
=
4
8
=
1
2
fifth term
a
r
4
=
8
×
(
1
2
)
4
=
8
×
1
16
=
1
2
7.The terms of the GP are
The first term is
u
1
=
a
=
3
The third term is
u
3
=
a
r
2
=
4
3
where the common ratio is
=
r
Therefore,
u
3
u
1
=
a
r
2
a
=
r
2
=
4
3
⋅
1
3
=
4
9
Therefore,
The common ratio is
r
=
√
4
9
=
2
3
The fifth term is
u
5
=
a
r
4
=
3
⋅
(
2
3
)
4
=
16
27
Step-by-step explanation:
Given:
6. The first term of a geometric sequence is 8, and the second term is 4.
7. The first term of a geometric sequence is 3, and the third term is 4/3.
To find: 6. The fifth term
7. The fifth term
Solution: nth term of a geometric progression is given by: an = ar^(n-1).
6. For the first term of the geometric sequence,
a₁ = ar^(1-1)
⇒ 8 = ar⁰
⇒ a = 8
For the second term of the geometric sequence,
a₂ = ar^(2-1)
⇒ 4 = ar
⇒ 4 = 8 × r (substituting the value of a from the previous equation)
⇒ r = 1/2
Therefore, the fifth term of the geometric sequence
= ar^(5-1)
= 8 × (1/2)⁴
= 8 × 1/16
= 1/2
7. For the first term of the geometric sequence,
a₁ = ar^(1-1)
⇒ 3 = ar⁰
⇒ a = 3
For the third term of the geometric sequence,
a₂ = ar^(3-1)
⇒ 4/3 = ar²
⇒ 4/3 = 3 × r² (substituting the value of a from the previous equation)
⇒ r² = 4/9
⇒ r = 2/3
Therefore, the fifth term of the geometric sequence
= ar^(5-1)
= 3 × (2/3)⁴
= 3 × 16/81
= 16/27
Answer: 6. a. 1/2
7. c. 16.27