find the first five terms of each geometric sequence in which a1=4, r=-2
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Step-by-step explanation:
The general term for a geometric sequence is
a
n
=
a
1
r
n
−
1
Where
a
n
is the nth term,
a
1
is first term
r
is the common ratio and
n
is the position or number of the term.
Here
a
1
=
8
and
r
=
5
Put
n
=
2
⇒
a
2
=
8
⋅
5
2
−
1
=
8
⋅
5
=
40
Put
n
=
3
⇒
a
3
=
8
⋅
5
3
−
1
=
8
⋅
5
2
=
8
⋅
25
=
200
Put
n
=
4
⇒
a
4
=
8
⋅
5
4
−
1
=
8
⋅
5
3
=
8
⋅
125
=
1000
Put n=5
⇒a5=8.55−1=8.54=8×⋅625=5000
Hence, the first five terms of the given geometric sequence are
8,40,200,1000 50
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