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babymother [125]
2 years ago
8

Need help geometric sequences see pic for details

Mathematics
1 answer:
LenKa [72]2 years ago
5 0

Given:

The recursive formula of a geometric sequence is

a_n=a_{n-1}\cdot (\dfrac{1}{8})

a_1=-3

To find:

The explicit formula of the given geometric sequence.

Solution:

We know that, first term of geometric sequence is a_1=-3.

Recursive formula of a geometric sequence is

a_n=a_{n-1}\times r      ...(i)

where, r is common ratio.

We have,

a_n=a_{n-1}\cdot (\dfrac{1}{8})    ...(ii)

On comparing (i) and (ii), we get

r=\dfrac{1}{8}

The explicit formula of a geometric sequence is

a_n=a_1r^{n-1}

Putting a_1=-3 and r=\dfrac{1}{8}, we get

a_n=-3\left(\dfrac{1}{8}\right)^{n-1}

Therefore, the correct option is D.

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https://youtu.be/WYNfQabLpuk

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