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

$3660$

Steps to Solve

Identify the Differences

Calculate the differences between consecutive terms in the series.

Between 456 and 577: $$ 577 - 456 = 121 $$
Between 577 and 1018: $$ 1018 - 577 = 441 $$
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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