Question

Which sequence is modeled by the graph below ?

Answer 1

Answer:

Geometric Sequence.

$a_{n}=(2)^{n-1}$

Step-by-step explanation:

The x-coordinates represent the number of terms of the sequence while the y-coordinates represent the term of the sequence. So the series shown on the graph is:

1, 2, 4, 8

We can see that the ratio of two consecutive terms of the above sequence is constant. i.e.

2/1 = 2

4/2 = 2

8/4 = 2

Such a sequence in which the ratio of two consecutive terms is a constant is known as Geometric Sequence and this constant ratio is known as common ratio.

The general term of a geometric sequence is represented as:

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

Using the values for the given sequence we get:

$a_{n}=1(2)^{n-1}$

$a_{n}=(2)^{n-1}$

Where n represents the number of term.