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The second term of a geometric sequence is 2 and the last term is 8. If the common ratio is 2√, how many geometric means are there between the first term and the last term?

 Aug 12, 2015

Best Answer 

 #2
avatar+26396 
+5

The second term of a geometric sequence is 2 and the last term is 8. If the common ratio is 2√, how many geometric means are there between the first term and the last term?

 

t2=t1r1|t2=2 and r=2122=t1212t1=2212t1=2112t1=212

tn=t1rn1|tn=23 and t1=212 and r=21223=212212(n1)|1226=212n126=21+n126=2n6=nn=6

 

We have 6 terms, so between the first term and the 6th term are 4 terms.

 

t1=212=2t2=222=2t3=232=222212=22t4=242=22=4t5=252=242212=222=42t6=262=23=8

 

 Aug 12, 2015
 #1
avatar+118703 
+5

The second term of a geometric sequence is 2 and the last term is 8. If the common ratio is 2√, how many geometric means are there between the first term and the last term?

 

This is the sequence,

 

2,22,4,42,8

 

I am not sure what geometric mean means in relation to this question.  :/

 Aug 12, 2015
 #2
avatar+26396 
+5
Best Answer

The second term of a geometric sequence is 2 and the last term is 8. If the common ratio is 2√, how many geometric means are there between the first term and the last term?

 

t2=t1r1|t2=2 and r=2122=t1212t1=2212t1=2112t1=212

tn=t1rn1|tn=23 and t1=212 and r=21223=212212(n1)|1226=212n126=21+n126=2n6=nn=6

 

We have 6 terms, so between the first term and the 6th term are 4 terms.

 

t1=212=2t2=222=2t3=232=222212=22t4=242=22=4t5=252=242212=222=42t6=262=23=8

 

heureka Aug 12, 2015

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