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?
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=t1⋅r1|t2=2 and r=2122=t1⋅212t1=2⋅2−12t1=21−12t1=212
tn=t1⋅rn−1|tn=23 and t1=212 and r=21223=212⋅212⋅(n−1)|1226=21⋅2n−126=21+n−126=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=222⋅212=2⋅√2t4=242=22=4t5=252=242⋅212=22⋅√2=4⋅√2t6=262=23=8
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,
2,2√2,4,4√2,8
I am not sure what geometric mean means in relation to this question. :/
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=t1⋅r1|t2=2 and r=2122=t1⋅212t1=2⋅2−12t1=21−12t1=212
tn=t1⋅rn−1|tn=23 and t1=212 and r=21223=212⋅212⋅(n−1)|1226=21⋅2n−126=21+n−126=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=222⋅212=2⋅√2t4=242=22=4t5=252=242⋅212=22⋅√2=4⋅√2t6=262=23=8