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Natasha2012 [34]
3 years ago
5

Use the following explicit function to identify f(1) & r, and list the first five terms of the sequence.

Mathematics
2 answers:
shusha [124]3 years ago
7 0

Given:

The explicit function is:

To find:

and first 5 terms.

Solution:

The explicit formula a geometric sequence is:

           ...(i)

Where, a is the first term and r is the common ratio.

We have,

        ...(ii)

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

And,

For ,

For ,

Similarly, substituting , we get

Therefore,  and the first five terms are .

rjkz [21]3 years ago
5 0

Given:

The explicit function is:

f(n)=1000\left(\dfrac{1}{4}\right)^{n-1}

To find:

f(1)=?,r=? and first 5 terms.

Solution:

The explicit formula a geometric sequence is:

f(n)=ar^{n-1}            ...(i)

Where, a is the first term and r is the common ratio.

We have,

f(n)=1000\left(\dfrac{1}{4}\right)^{n-1}         ...(ii)

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

a=1000

f(1)=1000

And,

r=\dfrac{1}{4}

For n=1,

f(1)=1000\left(\dfrac{1}{4}\right)^{1-1}

f(1)=1000\left(\dfrac{1}{4}\right)^{0}

f(1)=1000(1)

f(1)=1000

For n=2,

f(2)=1000\left(\dfrac{1}{4}\right)^{2-1}

f(2)=1000\left(\dfrac{1}{4}\right)^{1}

f(2)=1000\times \dfrac{1}{4}

f(2)=250

Similarly, substituting n=3,4,5, we get

f(3)=62.5

f(4)=15.625

f(5)=3.90625

Therefore, f(1)=1000,r=\dfrac{1}{4} and the first five terms are 1000,250,62.5,15.625,3.90625.

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