Here, there are two alternating patterns.
The first begins with 17 and adds 2; the second begins with 32 and subtracts 3.

This is an alternating subtraction series in
which 2 is subtracted twice, then 3 is subtracted once, then 2 is subtracted twice, and so on.

This is a simple addition series with repetition. It adds 3 to each number to arrive at the next, which is repeated before 3 is added again.

75⁺²¹⁶, 291⁺¹²⁵,
416⁺⁶⁴,
480⁺²⁷, 507, __.The differences are cubes of consecutive natural numbers in decreasing order.Hence, the next number in the series in 507 + 2³ = 515.

12^*0.5, 6^*1, 6^*1.5, 9^*2, 18^*2.5, 45^*3, __.
The next number in the series is 45 * 3 = 135.

1027⁺⁴, 1031⁺⁶, 1037⁺⁸, 1045⁺⁹, 1054, __The differences are consecutive composite numbers in increasing order.Hence, the next number in the series in 1054 + 10 = 1064.

8^*2, 16^*3,
48^*2, 96^*3, 288^*2, 576, __
The numbers in the series are alternately being multiplied by two and three.Hence, the next number in the series in 576 * 3 = 1728.

75075⁺³, 25025⁺⁵,
5005⁺⁷, 715⁺¹¹, __, 5.The numbers are being divided by consecutive prime numbers. Hence, the next number in the series is 715 + 11 = 65.

12^{*3 - 1}, 35^{*3 + 1}, 106^{*3 - 1}, 317^{*3 + 1}, 952, __The next number in the series is 952 * 3 - 1 = 2855.

5^{*2 + 3}, 13^{*3 + 2}, 41^{*2 + 3}, 85^{*3 + 2}, 257^{*2 + 3}, __The next number in the series is 257 * 2 + 3 = 517.