The second term in a geometric sequence is 20. The fourth term in the same sequence is 45/4 or 11.25. What is the common ratio in this sequence?

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The second term in a geometric sequence is 20. The fourth term in the same sequence is 45/4 or 11.25. What is the common ratio in this sequence?

Mathematics
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well a term in a geometric sequence is found using \[a_{n} = a \times r^{n -1}\] and you know the 2nd term \[20 = a \times r^{2 -1} ~~~or~~~20 = a \times r\] and he 4th term \[\frac{45}{4} = a \times r^3\] which can be written as \[\frac{45}{4} = a \times r \times r^2\] make the substitution for the 2nd term \[\frac{45}{4} = 20 \times r^2\] now you can solve for r
and there are 2 possible answerz for r
Which are 1/7 and 3 right ?

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|dw:1437106434841:dw| so then simplify the fraction |dw:1437106495856:dw|
so take thhe square root of both sides... of the equation and you'll get the 2 answers
3/4 and 1/4 ?
well you are halfway correct |dw:1437107382618:dw|

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