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40 votes
40 votes
30-28-25-21-16 next number

User Fedterzi
by
2.9k points

2 Answers

17 votes
17 votes

Answer:

10

Explanation:

30 -2

28 -3

25 -4

21 -5

16 -6

= 10

User Unorsk
by
3.1k points
19 votes
19 votes

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

User Gi
by
3.2k points