Question

Is this sequence geometric? If so, identify the common ratio.

Answer 1

Yes, it is geometric and the ratio is 3/4.  You can tell because you can divide each one by the one before and you get 3/4.  (3/16)/(1/4)=3/4, (9/64)/(3/16)=3/4, and so on.

Hope that helps

Answer 2

Answer:  The correct option is (b) Yes, $\dfrac{3}{4}.$

Step-by-step explanation:  The given sequence is

$\dfrac{1}{4},~\dfrac{3}{16},~\dfrac{9}{64},~\dfrac{27}{256},~\dfrac{81}{1024},~.~.~.$

We are to check whether the given sequence is geometric. If so, we are to find the common ration.

GEOMETRIC SEQUENCE: A sequence of numbers where each term is found by multiplying by a constant with the preceding term. This constant is called the common ratio, r.

In the given sequence, we can see

$\dfrac{\frac{3}{16}}{\frac{1}{4}}=\dfrac{3}{4}~~~~\Rightarrow \dfrac{3}{16}=\dfrac{3}{4}\times \dfrac{1}{4},\\\\\\\dfrac{\frac{9}{64}}{\frac{3}{16}}=\dfrac{3}{4}~~~~\Rightarrow \dfrac{9}{64}=\dfrac{3}{4}\times \dfrac{3}{16},\\\\\\\dfrac{\frac{27}{256}}{\frac{9}{64}}=\dfrac{3}{4}~~~~\Rightarrow \dfrac{27}{256}=\dfrac{3}{4}\times \dfrac{9}{64},\\\\\\\dfrac{\frac{81}{1024}}{\frac{27}{256}}=\dfrac{3}{4}~~~~\Rightarrow \dfrac{81}{1024}=\dfrac{3}{4}\times \dfrac{27}{256},~etc$

Therefore, each term is found by multiplying $\dfrac{3}{4}$ with the preceding term.

Thus, the given sequence is geometric and its common ratio is $\dfrac{3}{4}$

Option (b) is correct.