We have been given the sequence 2,3,5,9,17.
We can write the terms of this sequence as

From the above term we can see that for the first term we take exponent 0 on 2 and then add 1 .
For second term we take exponent 1 on 2 and then add 1 .
For third term we take exponent 2 on 2 and then add 1 .
Using this fact for the next term of the sequence i.e. 6th term, we can take exponent 5 on 2 and then add 1 .
Therefore, next term of the sequence is given by

Therefore, the next term is 33.
Using the above facts, the pattern is given by

Answer:
Rule:

Step-by-step explanation:
<em>I will answer generally, since the coordinates of f, g and h are not given</em>
Given
Point: x, y
Translation Rule
1 : x + 3, y - 1
2: 90 degree counterclockwise
Required
Determine the new coordinates
<u>At the first translation of (x,y) by x + 3, y - 1</u>
The new point is: 
<u>At the second translation (90 degrees counterclockwise)</u>
When a point (x,y) is translated using this rule, it becomes (-y,x)
So, the new point is:


If the initial point of h is (2,3),
The new point is:


It's D: (0,0)
This is because when you put 0 in for x your y value will equal 0 and that is one of your answers, so it's the point (0,0)
B is going to be where A is