Sure, let's take a look at each sequence:
A. This sequence is increasing by 5 each time. So, to find the next three terms, we just add 5 to the most recent term three times. Starting at 20, we add 5 and get 25. We add 5 to 25 and get 30. We add 5 to 30 and get 35. So, the next three terms are 25, 30, and 35. The rule for this sequence is 5n, where n is the term number.
B. This sequence is increasing by 2 each term. So, again, we simply add 2 to the most recent term three times. Starting at 9, we add 2 and get 11. We add 2 to 11 and get 13. We add 2 to 13 and get 15. So, the next three terms are 11, 13, and 15. The rule for this sequence is 2n + 1, where n is the term number.
C. This sequence is a bit more complicated. It's decreasing each time, and each term is the result of taking the reciprocal of the term number plus 1. So, to find the next term, we take the term number, add one, and then find the reciprocal. The fifth term is 1/(5+1) = 1/6, or about 0.1667 when rounded to four decimal places. The sixth term is 1/(6+1) = 1/7, or about 0.142857 when rounded to six decimal places. The seventh term is 1/(7+1) = 1/8 or 0.125. So, the next three terms are 1/6, 1/7, and 1/8, or 0.1667, 0.142857, and 0.125 when rounded. The rule for this sequence is 1 / (n + 2), where n is the term number.