To find the area of a quarter circle, you simply take a quarter of a full circle. As all quarters are equal, this means that the formula would be <span><span>π<span><span>r2</span>4</span></span><span>π<span><span>r2</span>4</span></span></span><span>. But wait, there's more. If you notice, </span><span><span>π<span><span>r2</span>4</span>=π<span><span>r2</span>2</span></span><span>π<span><span>r2</span>4</span>=π<span><span>r2</span>2</span></span></span><span>. This coincides with the circle formula, just with half the radius. Notice anything? A quarter of a circle can be calculated in the same way a circle a quarter the size can. This means that a quarter circle is equal to a circle a quarter size. In this same way, a ninth of a circle is equal to a circle of one ninth the size.</span>
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

Looks like this
Everything in one picture