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The wildflowers at a national park have been decreasing in numbers. There were 1200 wildflowers in the first year that the park started tracking them. Since then, there have been one fourth as many new flowers each year. Create the sigma notation showing the infinite growth of the wildflowers and find the sum, if possible.

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Answer:

Step-by-step explanation:

We have total 1200 wildflowers in first year that is first term a  is 1200

We have to find sigma notation  showing the infinite growth of the wildflowers.

\(wildflowers=\sum_{i=1}^{\infty }1200(\frac{1}{4})^{i-1}\)

Formula for infinite sum of GP is \(S_{\infty}=\frac{a}{1-r}\)

Here, \(a=1200,r=\frac{1}{4}\)

On substituting the values in the formula of sum we get:

\(S_{\infty}=\frac{1200}{1-\frac{1}{4}}\)

On simplification we get:

\(S_{\infty}=\frac{1200}{\frac{3}{4}}=1600\)

Therefore, total sum of wildflowers 1600.

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