Question

The wildflowers at a national park have been decreasing in numbers. There were 300 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.

I chose C, but can someone check for me? Thanks :)

Answer 1

Choice C is correct. Do you need an explanation?

Answer 2

Answer: Third option is correct.

Explanation:

Since we have given that

Initial wildflowers in the first year = 1200

Every year, the number of wildflower is one fourth of the previous year.

So, it form a geometric series:

1200,300,75............

so, using sigma notation we can express the infinite growth of the wildflowers:

`\sum ^(\infty)_(i=1)1200((1)/(4))^(i-1)`

As we know that sum of infinite terms in case of geometric series is given by

`S_(\infty)=(a)/(1-r)\\\\S_(\infty)=(1200)/(1-0.25)\\\\S_(\infty)=(1200)/(0.75)\\\\S_(\infty)=1600`

Therefore, there are 1600 wildflowers.

Hence, Third option is correct.