Question

Which sequence is modeled by the graph below? coordinate plane showing the points 1, 2; 2, 4; 3, 8

Answer 1

First, we inspect what type of sequence is the order of the coordinates:
a2 = 1
a3 = 2
a4 = 4

Getting the difference,
a3 - a2 = 1
a4 - a3 = 2

The differences are not equal; hence, the sequence is not arithmetic.

Getting the ratio:
a3/a2 = 2
a4/a3 = 2

The common ratio is 2. Using the general form for a geometric series:
an = a1 r^(n-1)
If n = 2
1 = a1 (2)^(2-1)
a1 = 1/2

So,
an = (1/2) (2)^(n-1)

Answer 2

The sequence is given by
`a_n=2^n`.

Explanation:

We are given that,

The points representing the sequence graphically are (1,2), (2,4) and (3,8).

That is, in the ordered pair (x,y), the co-ordinate 'y' is the value of the x-th term of the sequence.

We get that,

(1,2) represents that the value of the 1st term of the sequence is 2.

(2,4) represents that the value of the 2nd term of the sequence is 4.

(3,8) represents that the value of the 3rd term of the sequence is 8.

That is, the sequence is given by,

`2, 4, 8,.....`

This sequence can be written as,

`2^1,2^2,2^3,.....`

So, the sequence is given by
`a_n=2^n`.