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heureka

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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?

 

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

 

12.08.2015