Answer: The required common ratio of the given geometric sequence is \(\dfrac{3}{2}.\)
Step-by-step explanation: We are given to find the common ratio of the following geometric sequence :
16, 24, 36, 54, . . .
We know that
the common ratio of a geometric sequence is the ratio of any term to its preceding term.
For the given sequence, we have
a(1) = 16, a(2) = 24, a(3) = 36, a(4) = 54, . . .
So, we get
\(\dfrac{a(2)}{a(1)}=\dfrac{24}{16}=\dfrac{3}{2},\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{36}{24}=\dfrac{3}{2},\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{54}{36}=\dfrac{3}{2},~~.~~.~~.\)
Thus, the required common ratio of the given geometric sequence is \(\dfrac{3}{2}.\)
