Question

The population of a local species of dragonfly can be found using an infinite geometric series where a1 = 42 and the common ratio is 3/4. Write the sum in sigma notation and calculate the sum that will be the upper limit of this population.

Answer 1

we are given

first term is

`a_1=42`

common ratio is

`r=(3)/(4)`

now, we can find nth term

`a_i=a_1(r)^(i-1)`

now, we can plug values

`a_i=42((3)/(4))^(i-1)`

now, we can write in sigma form

`sum=\sum _(i=1)^(\infty )\:42((3)/(4))^(i-1)`

now, we can find sum

we can use formula

`sum=(a)/(1-r)`

now, we can plug values

we get

`sum=(42)/(1-(3)/(4))`

`sum=168`

so, option-D.................Answer