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In a geometric sequence, the 23rd term is 16 and the 24th term is 1/4. What is the 30th term?

 Jun 16, 2024

Best Answer 

 #1
avatar+1950 
+1

We can define variables to solve this problem. 

Let's let the common ratio of this geometric sequence be r.

We have

16r=1/4r=(1/4)/16=1/64

 

So the common ratio is 1/64. 

 

Now, we calculate for the 30th term. We have'

(1/4)r6=(1/4)(1/64)6=(1/4)(1/43)6=(1/4)19=0.000000000003638

 

So our final answer is 0.000000000003638.

 

Thanks! :)

 Jun 16, 2024
 #1
avatar+1950 
+1
Best Answer

We can define variables to solve this problem. 

Let's let the common ratio of this geometric sequence be r.

We have

16r=1/4r=(1/4)/16=1/64

 

So the common ratio is 1/64. 

 

Now, we calculate for the 30th term. We have'

(1/4)r6=(1/4)(1/64)6=(1/4)(1/43)6=(1/4)19=0.000000000003638

 

So our final answer is 0.000000000003638.

 

Thanks! :)

NotThatSmart Jun 16, 2024

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