Question

How do you determine whether the ratios are equivalent: $3/4,24/32$ ?

Answer 1

Hint: We have been asked to verify whether the ratios of the given terms are equal or not $3/4,24/32$ . For doing that we will verify the ratio by simplifying the second term and comparing it with the first term.

Complete step-by-step solution:
Now considering from the question we have been asked to verify whether the ratios of the given terms $3/4,24/32$ is equal or not.
For doing that we will verify the ratio by simplifying the second term which is $24/32$ and comparing it with the first term which is $3/4$ .
So here we need to verify the ratio between different consecutive terms.
We will verify the ratio of $3/4,24/32$. The simplified form of $24/32$ is $\Rightarrow 24/32=3/4$ .
If we observe all the ratios are equal. Therefore these terms $3/4,24/32$ have a common ratio.
Since the given two terms have a common ratio we can say that they are part of a geometric sequence.

Note: This type of questions are very simple, involve less calculations, very few mistakes are possible and can be solved in a less span of time. We can also find the ${{n}^{th}}$ term of the sequence by using the formula given as $a{{r}^{n-1}}$ where $a$ is the first term and $r$ is the common ratio. If we assume that the given terms are first two terms of the sequence then ${{n}^{th}}$ term will be given as $\Rightarrow \left( 3/4 \right){{\left( 3/4 \right)}^{n-1}}$ .