How do you write an equation for the nth term of the geometric sequence #64,16,4,....#?

Answer 1

#64(1/4)^(n-1)#

This is a geometric sequence with starter

a = 64 and common ratio

r = 16/64=4/16=1/4 ..

The generall #(n^(th))# term is
#ar^(n-1)#
#=64(14)^(n-1)#

For exemplification,

the #4^(th)# term is #64(1/4)^3=64/64=1# and
the #10^(th)# term is #64(1/4)^9=64/262144=1/4096#.
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Answer 2

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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Answer from HIX Tutor

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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