Question

Wanahton purified a portion of water with 900 grams of contaminants. Each hour, a third of the contaminants was filtered out.

Let g(n) be the amount of contaminants (in grams) that remained by the beginning of the nth hour.

g is a sequence. What kind of sequence is it?

A. Arithmetic sequence

B. Geometric sequence

Write an explicit formula for the sequence.

g(n) = ?

Answer 1

Answer:

B. Geometric sequence.

$g(n)=900\cdot (\frac{2}{3})^{n-1}$

Step-by-step explanation:

We have been given that Wanahton purified a portion of water with 900 grams of contaminants. Each hour, a third of the contaminants was filtered out.

The amount of contaminants remaining after each hour would be 2/3 of the previous hour amount as 1/3 of contaminants was filtered.

Since amount is not constant, therefore, the sequence would be geometric.

We know that explicit formula for geometric sequence is in form $a(n)=a\cdot r^{n-1}$, where,

a = First term,

r = Common ratio.

For our given scenario $a=900$ and $r=\frac{2}{3}$, so our required formula would be:

$g(n)=900\cdot (\frac{2}{3})^{n-1}$

Therefore, an explicit formula for the given geometric sequence would be $g(n)=900\cdot (\frac{2}{3})^{n-1}$.