The next term in following series is 456, 577, 1018, 1979, ?
Understand the Problem
The question is asking for the next term in a given numerical series: 456, 577, 1018, 1979. It requires the identification of the pattern in the series to predict the following number.
Answer
$3660$
Answer for screen readers
The next term in the series is $3660$.
Steps to Solve
- Identify the Differences
Calculate the differences between consecutive terms in the series.
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Between 456 and 577: $$ 577 - 456 = 121 $$
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Between 577 and 1018: $$ 1018 - 577 = 441 $$
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Between 1018 and 1979: $$ 1979 - 1018 = 961 $$
- Analyze the Differences
Now we have the sequence of differences: 121, 441, 961.
Next, we need to identify a pattern in these differences.
- Find Patterns in Differences
Notice that:
- $121 = 11^2$
- $441 = 21^2$
- $961 = 31^2$
The differences are increasing by $10^2$, $20^2$, $30^2$.
- Calculate the Next Difference
Continuing this pattern, the next difference should be: $$ 41^2 = 1681 $$
- Find the Next Term
Add this difference to the last term in the original series: $$ 1979 + 1681 = 3660 $$
The next term in the series is $3660$.
More Information
The series follows a pattern where each difference is the square of consecutive multiples of 10 plus an incremental increase of 1 (i.e., $10^2$, $20^2$, $30^2$, $40^2$).
Tips
- Confusing the pattern in differences with simple addition or multiplication can lead to incorrect conclusions.
- Not properly squaring the increments could result in an error.
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