Question

The wildflowers at a national park have been increasing in numbers. There were 300 wildflowers in the first year that the park started tracking them. Since then, there has 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.

Answer 1

\[\Large\sum_{k=0}^\infty(300\times0.25^k)\]

Answer 2

Year New flowers

1 1200

2 300

3 75

Answer 3

@kc_kennylau

Answer 4

why 1200?

Answer 5

use geometric series

Answer 6

uhh how do i do that?

Answer 7

\[S=\frac a{1-r},\]where S is the sum, a is the first term and r is the rate.

Answer 8

ok

Answer 9

the rate is divide by 4 do i put that as the rate?

Answer 10

no, you put 0.25 as the rate.

Answer 11

why 0.25?

Answer 12

@kc_kennylau

Answer 13

because they increase in the rate of 1/4=0.25

Answer 14

so it would be 1200/0.25

Answer 15

@kc_kennylau

Answer 16

@kc_kennylau u there?

Answer 17

times

Answer 18

300

Answer 19

@mathmale

Answer 20

@perl

Answer 21

@perl

Answer 22

@perl

Answer 23

hello

Answer 24

i couldnt find the tag link

Answer 25

yes im here! finally!