Answer:
10
Explanation:
Given the sequence 30, 28, 25, 21, 16, you want to know the next number.
Differences
First differences between successive terms are ...
28 -30 = -2
25 -28 = -3
21 -25 = -4
16 -21 = -5
These are not constant, so this is not an arithmetic sequence. However, we notice the second differences are constant:
-3 -(-2) = -1
-4 -(-3) = -1
-5 -(-4) = -1
Application
This observation tells us the next second difference is ...
-5 +(-1) = -6
And the next number in sequence is ...
16 +(-6) = 10
The next number is 10.
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Additional comment
When a sequence of numbers is described by a polynomial or exponential, looking at differences (and their differences) can help determine the degree of the polynomial, or the common ratio of the exponential.
Here, the second differences are constant, so a second-degree (quadratic) polynomial will describe the sequence. The polynomial describing this sequence is ...
a(n) = 31 -(n)(n+1)/2