This is an alternating subtraction series with the interpolation of a random number 5 as every third number. In the subtraction series, 3 is subtracted, then 4, then 3, and so on.

Here, every other number follows a different pattern. In the first series, 6 is added to each number to arrive at the next. In the second series, 10 is added to each number to arrive at the next.

This is a simple subtraction series in which a random number 85 is interpolated as every third number. In the subtraction series, 10 is subtracted from each number to arrive at the next.

This is a subtraction series with repetition. Each number repeats itself and then decreases by 9.

This is an alternating addition series in which 10 is added, then 5, then 10, and so on.

This is an alternating subtraction series with repetition. There are two different patterns here. In the first, a number repeats itself; then 3 is added to that number to arrive at the next number, which also repeats. This gives the series 17, 17, 20, 20, 23, and so on. Every third number follows a second pattern, in which 3 is subtracted from each number to arrive at the next: 34, 31, 28.

This is an alternating repetition series in which a random number 61 is interpolated as every third number into an otherwise simple subtraction series. Starting with the second number, 57, each number (except 61) is 7 less than the previous number.

In this simple addition series, each number is 5 more than the previous number.

Here, is a simple addition series, which begins with 9 and adds 7.

This is an alternating addition series with a random number 4 interpolated as every third number. In the main series, 1 is added, then 2 is added, then 1, then 2, and so on.

This is an alternating repetition series, with a random number, 22, interpolated as every third number into an otherwise simple addition series. In the addition series, 4 is added to each number to arrive at the next number.

This is a simple alternating addition and subtraction series. First, 3 is added, then 1 is subtracted, then 3 is added, 1 subtracted, and so on.

This is an alternating addition and subtraction series. In the first pattern, 2 is added to each number to arrive at the next; in the alternate pattern, 6 is subtracted from each number to arrive at the next.

This is a simple subtraction series, in which 4 is subtracted from each number to arrive at the next.

In this simple subtraction series, the numbers decrease by 3.

1² + 2² = 5 2² + 3² = 13 3² + 4² = 25 4² + 5² = 41 5² + 6² =61 6² + 7² = 85 7² + 8² -=113 8² + 9² = 145

Here, there are two alternating patterns, one addition and one subtraction. The first starts with 2 and increases by 2; the second starts with 44 and decreases by 3.

In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number.

This is an alternating addition series that adds 5, then 2, then 5 and so on.

In this simple subtraction with repetition series, each number is repeated, then 3 is subtracted to give the next number, which is then repeated, and so on.

Two patterns alternate here, with every third number following the alternate pattern. In the main series, beginning with 4, 3 is added to each number to arrive at the next. In the alternating series, beginning with 26, 6 is subtracted from each number to arrive at the next.

This is an alternating addition and subtraction series in which the addition of 4 is alternated with the subtraction of 3.

There are two alternating patterns with every other number following a different pattern. The first pattern begins with 13 and adds 2 to each number to arrive at the next; the alternating pattern begins with 29 and subtracts 3 each time.

This simple addition series adds 4 to each number to arrive at the next.