5^*1, 5^*2, 10^*3, 30^*4, 120^*5, 600, __The next number in the series is 600 * 6 = 3600.

125^*3, 375⁺², 377^*3, 1131⁺², 1133, __.
The numbers are being alternatively multiplied by three and two is added.Hence, the next number in the series in 1133 * 3 = 3399.

12^*2-3,
21^*2-3,
39^*2-3,
75^*2-3, 147, __The next number in the series is 147^*2-3 = 291.

150, 392, 810, 1452, 2366, __=>5³ + 5²,
7³ + 7², 9³ + 9², 11³ + 11², 13³ + 13², __The next number in the series is 15³ + 15² = 3600.

6, 24, 60, 120, 210, __=>2³ - 2, 3³ - 3, 4³ - 4, 5³ - 5, 6³ - 6, __
The next number in the series is7³ - 7 = 336.

29, 29, 27, 23, 25, 19, 23, 17, __, __
The given series is an alternate series. The numbers in the alternate positions starting with 29 in the first position form a series of consecutive odd numbers in decreasing order.i.e. 29, 27, 25, 23, 21.The remaining numbers form a series of prime numbers in decreasing order starting with 29 i.e 29, 23, 19, 17, 13.Hence, the next two numbers in the series are 21 and 13 respectively.

5, 12, 13, 7, 14, 17, 9, 16, 19, 11, 18, 23, __, __, __The given series is a mixture of three different series. Every third number starting with 5 form a series of consecutive odd numbers in increasing order.Every third number starting with 12 form a series of consecutive earn numbers. Similarly, every third number starting with 13 form a series of consecutive prime numbers.5, 7, 9, 11, 13(odd number series) 12, 14, 16, 18, 20 (even number series)13, 17, 19, 23, 29 (prime number series)Hence, the next numbers in the series are 13, 20 and 29.

24, 625, 26, 729, 28, 841, __=> 24, 25², 26, 27², 28, 29², __The next number in the series is 30.

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No Explanation