Question

The population of a type of local bass can be found using an infinite geometric series where a1 = 72 and the common ratio is one fourth. Find the sum of this infinite series that will be the upper limit of this population.

Answer 1

96

Explanation:

Given that the population of a type of local bass can be found using an infinite geometric series.

I term a1 = 72

Common ratio r =
`(1)/(4)`

We know that sum of n terms of geometric series where |r|<1 is

`S_(n) =(a(1-r^n)/(1-r)`

Sum of infinite terms would be limit of this Sn as n tends to infinity.

When r <1 we have r^n will tend to 0 as n tends to infinity.

Hence Sum of infinite terms

=
`(a)/(1-r) =(72)/(1-(1)/(4) ) \\=96`

Sum of infinite series = 96

Answer 2

Sum of infinite sequence is given by S∞ = a/(1 - r); where a is the first term and r is the common ratio.
S∞ = 72/(1 - 1/4) = 72/(3/4) = 96.