nolikemath
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wha would be the next 2 numbers in the pattern 1,5,13,25
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number patterns
- Thread starter nolikemath
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wha would be the next 2 numbers in the pattern 1,5,13,25
1. Calculate the differences. You'll get an arithmetic sequence.
2. Augment the sequence of differences by 2 elements and use them to determine the following 2 elements of the given sequence.
HallsofIvy
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Because, as pappus says, the first differences are an arithmetic sequence, the second differences are constant. One thing that tells us is that the sequential numbers are a quadratic function of n: Write \(\displaystyle y(n)= an^2+ bn+ c\). Knowing that y(0)= c= 1, y(1)= a+ b+ c= 5, and y(2)= 4a+ 2b+ c= 13, you can solve for a, b, and c. Using those values, find y(3) as a check (it should be equal to 25), then find y(4) and y(5).
Hello, nolikemath!
Look at the "gaps" between the numbers . . .
. . \(\displaystyle \begin{array}{ccccccccccc} \text{Sequence:} &1 && 5 && 13 && 25 & \cdots \\ \hline \text{Gaps:} && 4 && 8 && 12 & \cdots\end{array}\)
The gaps are increasing by 4 each time.
The next two gaps are 16 and 20.
The next two terms are: .\(\displaystyle \begin{Bmatrix} 25 + 16 &=& 41 \\ 41 + 20 &=& 61 \end{Bmatrix}\)
What would be the next 2 numbers in the pattern? .1, 5, 13, 25, . . .
Look at the "gaps" between the numbers . . .
. . \(\displaystyle \begin{array}{ccccccccccc} \text{Sequence:} &1 && 5 && 13 && 25 & \cdots \\ \hline \text{Gaps:} && 4 && 8 && 12 & \cdots\end{array}\)
The gaps are increasing by 4 each time.
The next two gaps are 16 and 20.
The next two terms are: .\(\displaystyle \begin{Bmatrix} 25 + 16 &=& 41 \\ 41 + 20 &=& 61 \end{Bmatrix}\)