# SSAT Upper Level Math : How to find algebraic patterns

## Example Questions

← Previous 1 3

### Example Question #1 : How To Find Algebraic Patterns

Find the sum of this infinite geometric series:

Explanation:

The sum of an infinite series with first term  and common ratio  is

Set , and evaluate:

### Example Question #1 : Algebra

Give the next number in the following sequence:

_____

Explanation:

The sequence is generated by alternately adding 2, then multiplying by 2:

, which is the correct choice.

### Example Question #1 : Algebra

Define an operation on the real numbers as follows:

Find the value of  that makes this statement true:

There is no such value of .

Explanation:

Replace  in the defintiion:

Now, set this equal to 32 and solve for :

### Example Question #4 : Algebra

What number replaces the circle?

Explanation:

The sequence is formed by alternately multiplying by a number, then adding the same number; the number incrementally increases every other term.

, the number which replaces the square.

, the number which replaces the circle.

### Example Question #1 : Algebra

is defined as the greatest integer less than or equal to .

Evaluate the expression for :

Explanation:

Substitute:

### Example Question #1 : How To Find Algebraic Patterns

is defined as the least integer greater than or equal to .

Evaluate for  :

Explanation:

Substitute :

### Example Question #1 : Algebra

What number replaces the circle in this sequence?

Explanation:

This sequence is alternately generated by subtracting two and multiplying by two.

We can therefore find the numbers that replace the square and the circle by reversing the pattern - alternately dividing by two and adding two beginning at 36:

- this replaces the circle

- this replaces the square

### Example Question #1 : Patterns

In the following number sequence, what number goes in place of the circle?

Explanation:

The sequence comprises the squares of the odd integers, in order:

...

The next number, which replaces the circle, is

.

### Example Question #1 : How To Find Algebraic Patterns

Define an operation on the set of real numbers as follows:

Evaluate:

The expression is undefined.

Explanation:

### Example Question #10 : Algebra

In the following number sequence, what number goes in place of the circle?