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

Answer:

The correct option is B

Step-by-step explanation:

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

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

$\sum_{i=1}^{\infty}a_1\cdot(r)^{i-1}\\\\\implies Sum = \sum_{i=1}^{\infty}48\cdot(\frac{1}{4})^{i-1}$

Therefore, The correct option is B