What is the common ratio of the geometric sequence whose second and fourth terms are 6 and 54, respectively?

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@iGreen
@nincompoop
@anonymous_user

Question

What is the common ratio of the geometric sequence whose second and fourth terms are 6 and 54, respectively?

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@iGreen 
@nincompoop 
@anonymous_user

anonymous · Answer

@LunyMoony

cwrw238 · Answer

4th term  = a1* r^3
2nd term  = a1*  r                     whre  r = common ratio
so r^2  = 4th term / 2nd term  = 54 / 6

cwrw238 · Answer

r^2 =  9 
r = 3

anonymous · Answer

you there @LunyMoony

anonymous · Answer

so the answer would be 3?

lunymoony · Answer

Yes, sry I passed these a while ago in geometry but never really understood them, so i was browsing the internet to learn them better

lunymoony · Answer

its 2 or 3, cwrw says it is 3 so I believe it is 3

anonymous · Answer

thanks :) i have a few more questions can you help with? Which sequence is geometric and has 14 as its fifth term and 12 as the common ratio?

    …, 1, 12, 14, 18, …

    …, 14, 12,  1, 2,…

    …, 172, 136,118, 19, …

    …, 8,  4,  2,  1, …

cwrw238 · Answer

5th term = a1 * r^4   where a1 = first term and r = common ration

cwrw238 · Answer

none of those sequences have a common ratio of 12  
- each term of the series is 12 times the previous if r = 12

cwrw238 · Answer

eg 1, 12, 144 ...             has  r = 12

cwrw238 · Answer

the only sequence in the list which is a GS is the last one  with a common ratio of 1/2

lunymoony · Answer

cwrw answered that question @lexikaylynn