This question is testing ones ability to recognize sequences as functions. 

For the purpose of Common Core Standards, sequences fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONENT.HSF-IF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the pattern of the given sequence.

For this particular problem, the common difference needs to be calculated as it is an arithmetic sequence.

$\displaystyle 1, 5, 9, \square, \triangle$

To identify the pattern or in other words, calculate the common difference, subtract the first term from the second term. Then subtract the second term from the third term. For an arithmetic sequence these two differences should be equal to one another.

$\displaystyle \\a_1,a_2,a_3,... \\a_2-a_1=d \\a_3-a_2=d$

Given this particular sequence 

$\displaystyle 1, 5, 9, \square, \triangle$

$\displaystyle a_1=1, a_2=5,a_3=9$

the common difference using the above method is as follows.

$\displaystyle \\a_1,a_2,a_3,... \\5-1=4 \\9-5=4 \\ \textup{Common Difference}=4$

Step 2: Find the value of the square.

To find the value of the square add the common difference to the previous term in the sequence.

$\displaystyle 1, 5, 9, \square, \triangle$

The term before the square is nine, therefore the value of the square is,

$\displaystyle 9+4=13\Rightarrow \square=13$.

The sequence is now,

$\displaystyle 1, 5, 9, 13, \triangle$

Step 3: Find the value of the triangle.

To find the value of the triangle add the common difference to the previous term in the sequence.

$\displaystyle 13+4=17\Rightarrow \triangle=17$

This question is testing ones ability to recognize sequences as functions. 

For the purpose of Common Core Standards, sequences fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONENT.HSF-IF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the pattern of the given sequence.

For this particular problem, the common ratio needs to be calculated as it is an geometric sequence.

$\displaystyle 1,7,49,...$

To identify the pattern or in other words, calculate the common ratio, divide the second term by the first term. Then divide the third term by the second term. For an geometric sequence these two ratios should be equal to one another.

$\displaystyle \\a_1,a_2,a_3,... \\ \\ \frac{a_2}{a_1}=d \\ \\ \frac{a_3}{a_2}=d$

Given this particular sequence 

$\displaystyle 1,7,49,...$

$\displaystyle a_1=1, a_2=7,a_3=49$

the common ratio using the above method is as follows.

$\displaystyle \\a_1,a_2,a_3,... \\ \\ \frac{7}{1}=7 \\ \\ \frac{49}{7}=7 \\ \textup{Common Difference}=7$

Step 2: Find the next value.

To find the value of the next term multiply the common ratio to the previous term in the sequence.

$\displaystyle 1,7,49,...$

The last term is 49, therefore the value of the next term is,

$\displaystyle 49\times 7=343$.

The sequence is now,

$\displaystyle 1,7,49,343,...$

Step 3: Find the next value.

To find the value of the next term multiply the common ratio to the previous term in the sequence.

$\displaystyle 343\times 7=2401$

Step 4: Answer the question.

The next two terms in the sequence are, $\displaystyle 343, 2401$.