Question

The population of a local species of beetle can be found using an infinite geometric series where a1 = 880 and the common ratio is one fourth. Write the sum in sigma notation, and calculate the sum (if possible) that will be the upper limit of this population.

Answer 1

the formula is a(1) ÷ (1 - r)
so 880 ÷ (1 - 1/4) = 880 ÷ (3/4) =1173 1/3

Answer 2

Answer: The sum would be 1173.3333....

Explanation:

Since we have given that

a₁ = 880

r =
`(1)/(4)`

We need to find the sum in sigma notation;

`\sum a_n=(a_1)/(1-r)`

And we need to calculate the sum that will be the upper limit of this population:

`\sum a_n=(880)/(1-(1)/(4))=(880)/((3)/(4))=(880* 4)/(3)=1173.3`

Hence, the sum would be 1173.3333....