12 13 17 26 42 ?

Options

A. 57
B. 58
C. 59
D. None of these

Answer

To solve the series: 12, 13, 17, 26, 42, ?, we need to identify the pattern in the differences between the consecutive numbers.

**Step 1: Calculate the differences between consecutive terms.**

- From 12 to 13:
\( 13 - 12 = 1 \)

- From 13 to 17:
\( 17 - 13 = 4 \)

- From 17 to 26:
\( 26 - 17 = 9 \)

- From 26 to 42:
\( 42 - 26 = 16 \)

So, the differences are:
1, 4, 9, 16

**Step 2: Identify the pattern in the differences.**

The differences are:
1 (which is \(1^2\)),
4 (which is \(2^2\)),
9 (which is \(3^2\)),
16 (which is \(4^2\)).

This suggests that the next difference should be \(5^2\), which is 25.

**Step 3: Add the next difference to the last term in the series.**

Now, we add this difference to the last term (42):
\( 42 + 25 = 67 \)

**Step 4: Conclusion**

Thus, the next term in the series is 67.

The answer is **67**, which corresponds to the option "none of these".

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