Complete the series: 5, 13, 45, 189, 957, ____ ?

To complete the series 5, 13, 45, 189, 957, we need to identify the pattern or rule governing the sequence.

Let's look at the differences between consecutive terms:

13 - 5 = 8 45 - 13 = 32 189 - 45 = 144 957 - 189 = 768

The differences between the consecutive terms are not consistent. Therefore, the series does not follow a simple arithmetic or geometric progression.

However, if we look at the differences between the differences, we can see a pattern:

32 - 8 = 24 144 - 32 = 112 768 - 144 = 624

The differences between the differences are increasing by a factor of 3. Therefore, we can assume that the next difference should be 624 * 3 = 1872.

Now, let's calculate the next term in the series:

957 + 1872 = 2829

Among the given options, none of them match the calculated value of 2829. Therefore, none of the given options is the correct answer.

It's possible that there is a mistake in the given series, or the series follows a pattern that is not immediately obvious.

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