How do you write an equation for the nth term of the geometric sequence #64,16,4,....#?
This is a geometric sequence with starter
a = 64 and common ratio
r = 16/64=4/16=1/4 ..
For exemplification,
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To write an equation for the (n)th term of a geometric sequence, we use the formula:
[ a_n = a_1 \times r^{(n-1)} ]
Where:
- ( a_n ) represents the (n)th term of the sequence.
- ( a_1 ) is the first term of the sequence.
- ( r ) is the common ratio of the sequence.
Given the geometric sequence (64, 16, 4, \ldots), we can determine ( a_1 ) and ( r ) as follows:
First term ( (a_1) ): (64)
Second term: (16)
To find the common ratio ( (r) ), divide the second term by the first term:
[ r = \frac{16}{64} = \frac{1}{4} ]
Now that we have ( a_1 = 64 ) and ( r = \frac{1}{4} ), we can write the equation for the (n)th term (( a_n )) of the sequence:
[ a_n = 64 \times \left(\frac{1}{4}\right)^{(n-1)} ]
Therefore, the equation for the (n)th term of the given geometric sequence is:
[ a_n = 64 \times \left(\frac{1}{4}\right)^{(n-1)} ]
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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