Note: The third term of the sequence should be [tex]\dfrac{27}{2}[/tex] instead of [tex]\dfrac{37}{2}[/tex], otherwise the sequence has no common ratio.
Given:
The given sequence is
[tex]24,18,\dfrac{27}{2},\dfrac{81}{8}[/tex]
To find:
The common ratio of the given sequence.
Solution:
The quotient of each pair of consecutive terms are:
[tex]\dfrac{18}{24}=\dfrac{3}{4}[/tex]
Similarly,
[tex]\dfrac{\dfrac{27}{2}}{18}=\dfrac{27}{36}[/tex]
[tex]\dfrac{\dfrac{27}{2}}{18}=\dfrac{3}{4}[/tex]
And,
[tex]\dfrac{\dfrac{81}{8}}{\dfrac{27}{2}}=\dfrac{81}{8}\times \dfrac{2}{27}[/tex]
[tex]\dfrac{\dfrac{81}{8}}{\dfrac{27}{2}}=\dfrac{3}{4}[/tex]
Therefore, the common ratio of the given sequence is [tex]\dfrac{3}{4}[/tex] or 0.75.
