Question

Find the common ratio 24,18,37/2,81/8

Answer 1

Note: The third term of the sequence should be $\dfrac{27}{2}$ instead of $\dfrac{37}{2}$, otherwise the sequence has no common ratio.

Given:

The given sequence is

$24,18,\dfrac{27}{2},\dfrac{81}{8}$

To find:

The common ratio of the given sequence.

Solution:

The quotient of each pair of consecutive terms are:

$\dfrac{18}{24}=\dfrac{3}{4}$

Similarly,

$\dfrac{\dfrac{27}{2}}{18}=\dfrac{27}{36}$

$\dfrac{\dfrac{27}{2}}{18}=\dfrac{3}{4}$

And,

$\dfrac{\dfrac{81}{8}}{\dfrac{27}{2}}=\dfrac{81}{8}\times \dfrac{2}{27}$

$\dfrac{\dfrac{81}{8}}{\dfrac{27}{2}}=\dfrac{3}{4}$

Therefore, the common ratio of the given sequence is $\dfrac{3}{4}$ or 0.75.