9514 1404 393
Answer:
95
Explanation:
The sequence of first differences is ...
32 -25 = 7
37 -32 = 5
47 -37 = 10
58 -47 = 11
71 -58 = 13
79 -71 = 8
These seem to have no pattern, so the sequence is not arithmetic, geometric, quadratic, or any other common type.
If we look at the digits of the numbers in the series, we see they have sums of ...
2 +5 = 7
3 +2 = 5
3 +7 = 10
4 +7 = 11
5 +8 = 13
7 +1 = 8
7 +9 = 16
That is, the difference between a number and the next in sequence appears to be the sum of the digits of the number. This rule tells us the next number is ...
79 +(7+9) = 95 . . . next number in sequence
_____
Additional comment
Sometimes, finding the rule is as much a right-brain activity as it is one of logic or deduction. Often, it is not obvious or easy. Questions like this one are intended to help you learn to think "out of the box."