Question

Which sequence is modeled by the graph below ?

Answer 1

Geometric Sequence.

`a_(n)=(2)^(n-1)`

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.