Answer:
An explicit formula for the given geometric sequence, a_{n} =\dfrac{-8}{5} (5)^{n}a
n
=
5
−8
(5)
n
Step-by-step explanation:
The given geometric sequence:
- 8, - 40, - 200, - 1000
Here, first term(a) = - 8, common ration(r) = \dfrac{-40}{-8}
−8
−40
= 5
To find, an explicit formula for the given geometric sequence = ?
We know that,
The explicit formula for the geometric sequence
a_{n} =ar^{n-1}a
n
=ar
n−1
∴ An explicit formula for the given geometric sequence
a_{n} =(-8)(5)^{n-1}a
n
=(−8)(5)
n−1
a_{n} =\dfrac{-8}{5} (5)^{n}a
n
=
5
−8
(5)
n
∴ An explicit formula for the given geometric sequence, a_{n} =\dfrac{-8}{5} (5)^{n}a
n
=
5
−8
(5)
n
hope it helps
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