There are infinitely polynomials of order 3 that will give these as the first three numbers and any one of these could be "the" rule. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
Here, the simplest solution, based on a polynomial of order 2, is
t(n) = 2.5* (-5*n^2 + 19*n - 8) for n = 1, 2, 3, ...
75The number which best completes the sequence 10 30 15 16 48 24 25 is 75.
10 30 15 16 48 24 25 75...
25
This is actually two sequences staggered back and forth: 1 4 9 16 25 1 3 6 10 As you can see, the first sequence is a series of perfect squares, and the second sequence is a series with a rate of change that is increasing by increments of one. The next number in the original sequence will be from the second series, making it 10 + 5, or 15. The sequence as a whole then continues like so: 1 1 4 3 9 6 16 10 25 15 36 21 49 28 64 36 81 45 100 ...
75.
75The number which best completes the sequence 10 30 15 16 48 24 25 is 75.
10 30 15 16 48 24 25 75...
25 It is the Fibonacci sequence multiplied by 5.
75
75
25
Nn
This is actually two sequences staggered back and forth: 1 4 9 16 25 1 3 6 10 As you can see, the first sequence is a series of perfect squares, and the second sequence is a series with a rate of change that is increasing by increments of one. The next number in the original sequence will be from the second series, making it 10 + 5, or 15. The sequence as a whole then continues like so: 1 1 4 3 9 6 16 10 25 15 36 21 49 28 64 36 81 45 100 ...
75
The nth term is: 5n
75.
The next answer in the sequence is 75 The sequence is times 3, divided by 2, plus 1 Example 10*3=30 30/2=15 15+1=16 16*3=48 48/2=24 24+1=25 25*3=75