What will be the next term ofthe series 13,17,27,49,89,...(a)153(b)142(c) 169(d)129

The given series is 13, 17, 27, 49, 89.

To find the pattern, let's look at the differences between consecutive terms:

17 - 13 = 4 27 - 17 = 10 49 - 27 = 22 89 - 49 = 40

The differences between the terms are not constant, so this is not an arithmetic sequence. However, the differences themselves (4, 10, 22, 40) seem to form a pattern. They are increasing by multiples of 6:

10 - 4 = 6 22 - 10 = 12 40 - 22 = 18

So, the next difference should be 18 + 6 = 24.

Adding this difference to the last term of the original series gives:

89 + 24 = 113

So, the next term in the series should be 113. However, this option is not given in the choices (a)153 (b)142 (c) 169 (d)129.

It seems there might be a mistake in the question or the provided options.

The given series is 13, 17, 27, 49, 89.

To find the pattern, let's look at the differences between consecutive terms:

17 - 13 = 4 27 - 17 = 10 49 - 27 = 22 89 - 49 = 40

The differences between the terms are not constant, so this is not an arithmetic sequence. However, the differences themselves (4, 10, 22, 40) seem to form a pattern. They are increasing by multiples of 6:

10 - 4 = 6 22 - 10 = 12 40 - 22 = 18

So, the difference between the next term and 89 should be 40 + 24 = 64 (since 24 is the next multiple of 6).

Therefore, the next term of the series should be 89 + 64 = 153.

So, the answer is (a) 153.