Question

The sequence below shows the number of bacteria Arjun observed each hour for a science experiment 5,20,80,320,1,280 which recursive function describes the number of bacteria observed at the nth hour

Answer 1

Answer:

$a_{n}=5*4^{n-1}$

Step-by-step explanation:

As the given sequence is a geometric sequence there will be a common ratio which can be obtained by dividing the next term by previous term

For the given sequence

$r = \frac{20}{5}\\ r=4$

The general for geometric sequence is:

$a_{n}=a_{1}r^{n-1}$

here a1 is the first term and r is the common ration

So, putting the values of r and a1, the geenral function for the given sequence is:

$a_{n}=5*4^{n-1}$

Answer 2

The recursive function describes the number of bacteria observed at the nth hour is; aₙ = 5 * (4)ⁿ ⁻ ¹

How to Solve Geometric Sequence?

We are given the geometric sequence as; 5, 20, 80, 320, 1,280

We know that the general formula to find the nth term of a geometric sequence is; aₙ = arⁿ ⁻ ¹

Where;

a is first term

r is common ratio

Thus, the recursive function is;

aₙ = 5 * (4)ⁿ ⁻ ¹

Read more about Geometric Sequence at; https://brainly.com/question/24643676

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