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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+1252 
+1

We can define variables to solve this problem. 

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

We have

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

 

So the common ratio is 1/64. 

 

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

\( (1/4) r^6 = (1/4)(1/64)^6\\ = (1/4) ( 1/4^3) ^6 \\ =(1/ 4)^19\\ =0.000000000003638\)

 

So our final answer is 0.000000000003638.

 

Thanks! :)

 Jun 16, 2024
 #1
avatar+1252 
+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

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

 

So the common ratio is 1/64. 

 

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

\( (1/4) r^6 = (1/4)(1/64)^6\\ = (1/4) ( 1/4^3) ^6 \\ =(1/ 4)^19\\ =0.000000000003638\)

 

So our final answer is 0.000000000003638.

 

Thanks! :)

NotThatSmart Jun 16, 2024

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