Answer: The required common ratio is 0.79.
Step-by-step explanation: Given that in a geometric series, each term is 21% less than the previous term.
We are to find the common ratio r for this geometric series.
Let the first term of the give geometric series be a.
Then, according to the given information, the second term of the geometric series will be
[tex]a_2=a-21\%\times a=a-\dfrac{21}{100}a=\dfrac{100-21}{100}a=\dfrac{79}{100}a=0.79a.[/tex]
Therefore, the required common ratio for the given geometric series is given by
[tex]r=\dfrac{0.79a}{a}=0.79.[/tex]
Thus, the required common ratio is 0.79.
The value of r in a geometric series is 0.79
A geometric series is one in that the ratio of each two successive terms is a constant function of the summation index.
From the given information;
[tex]\mathbf{a_2 = a -\dfrac{21}{100}(a)}[/tex]
[tex]\mathbf{a_2 =0.79a}[/tex]
The value of the common ratio (r) in a geometric series is calculated by using the formula;
[tex]\mathbf{r = \dfrac{a_2}{a_}}[/tex]
[tex]\mathbf{r = \dfrac{0.79a}{a_}}[/tex]
r = 0.79
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