6, 7.8, 10.1, 12.9, 16.2, ?
Understand the Problem
The question is asking for the next number in the given sequence. The numbers seem to follow a pattern, and we will analyze the differences between consecutive numbers to find the next value in the series.
Answer
The next number in the sequence is $20$.
Answer for screen readers
The next number in the sequence is $20$.
Steps to Solve
- Identify the given sequence
The numbers in the sequence are:
$6, 7.8, 10.1, 12.9, 16.2$
- Calculate the differences
Next, we calculate the differences between consecutive terms:
- $7.8 - 6 = 1.8$
- $10.1 - 7.8 = 2.3$
- $12.9 - 10.1 = 2.8$
- $16.2 - 12.9 = 3.3$
So, the differences are:
$1.8, 2.3, 2.8, 3.3$
- Calculate the differences of differences
Now, let's find the differences of these differences:
- $2.3 - 1.8 = 0.5$
- $2.8 - 2.3 = 0.5$
- $3.3 - 2.8 = 0.5$
The second differences are constant:
$0.5, 0.5, 0.5$
- Predict the next difference
Since the second differences are constant, we can predict the next difference in the first series:
Next difference = Last difference + Constant = $3.3 + 0.5 = 3.8$
- Calculate the next number in the sequence
Now, add this predicted difference to the last number in the sequence:
Next number = $16.2 + 3.8 = 20$
The next number in the sequence is $20$.
More Information
The sequence follows a quadratic pattern where the first differences increase by a constant value (0.5). This method is useful in identifying values in sequences that aren’t linear.
Tips
- Failing to calculate differences correctly. Always verify each step carefully.
- Overlooking the pattern of second differences. Ensure to check if they are constant for quadratic sequences.
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