This is an alternating addition and subtraction series. Roman numbers alternate with Arabic numbers. In the Roman numeral pattern, each number decreases by 1. In the Arabic numeral pattern, each number increases by 1.

This is a simple subtraction series. Each number is 35 less than the previous number.

This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.

Hence, 7 +3 10 -2 8 +3 11 -2 9 +3 12 -2 10

In this alternating repetition series, a random number, 33, is interpolated every third number into a simple addition series, in which each number increases by 2.

Here we see ups and downs in the series so there is a chance of 2 separate series
We can have 20 24 30 38 as one series
And 4 64 196 as other series.
Both series occur alternately so next term has to be of the second series.
In first series difference is
24 – 20 = 4
30 – 24 = 6
38 – 30 = 8
So, difference increases by 2
In second series, We see they are squares i.e. 2², 8², 14²
8-2 = 6
14-8 = 6
So next number, ? – 14 has to be = 6
So, ? = 14+6 = 20
So next term is 20² = 400

First term → 9

Second term → (9 *2 -1) = 17

Third term → (17 *2 -1) = 33

Fourth term → (33 *2 -1) = 65

Fifth term → (65 *2 -1) = 129

496 – 492 = 4 = 2²
492 – 483 = 9 = 3²
483 – 467 = 16 = 4²
So, the next has to be a difference of 25 = 5²
467 – 25 = 442

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

5
5 x 3 + 6 = 21
21 x 3 + 6 = 69
69 x 3 + 6 = 213
213 x 3 + 6 = 645
645 x 3 + 6 = 1941