Question

The population of a local species of dragonfly can be found using an infinite geometric series where a1 = 48 and the common ratio is 1/4 . Write the sum in sigma notation and calculate the sum that will be the upper limit of this population.

Answer 1

I think the letter is b but i am not sure

Answer 2

The correct option is B

Explanation:

`\text{First term, }a_1 = 48\\\\\text{Common Ratio,r = }(1)/(4)\\\\\text{The sum of the geometric progression is given by :}\\\\Sum = (a_1)/((1-r))\\\\\implies Sum=(48)/((1-(1)/(4)))\\\\\implies Sum = 48* (4)/(3)=64`

And the sigma notation for the above sum can be written as :

`\sum_(i=1)^(\infty)a_1\cdot(r)^(i-1)\\\\\implies Sum = \sum_(i=1)^(\infty)48\cdot((1)/(4))^(i-1)`

Therefore, The correct option is B