What will come in the place of question mark in the series 2, 7 ,14, 23, ? ,47 ?

Options

A. 28
B. 34
C. 31
D. 38

Answer

To find the missing number in the series 2, 7, 14, 23, ?, 47, we can analyze the differences between consecutive terms.

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

- The difference between 7 and 2 is:
\( 7 - 2 = 5 \)

- The difference between 14 and 7 is:
\( 14 - 7 = 7 \)

- The difference between 23 and 14 is:
\( 23 - 14 = 9 \)

- The difference between 47 and 23 is:
\( 47 - 23 = 24 \)

So, we have the differences:
5, 7, 9, ?, 24

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

The differences we have so far are:
5, 7, 9

These differences are increasing by 2 each time:
- From 5 to 7, the increase is 2.
- From 7 to 9, the increase is also 2.

Following this pattern, the next difference should be:
\( 9 + 2 = 11 \)

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

Now, we add this difference (11) to the last known term (23) to find the missing term:
\( 23 + 11 = 34 \)

**Step 4: Verify the next term.**

Now, we can check if this fits with the next term (47). The difference between 47 and 34 should also follow the pattern:
\( 47 - 34 = 13 \)

Now, we can see that the differences are:
5, 7, 9, 11, 13 (which are all odd numbers increasing by 2).

**Conclusion:**

Thus, the missing number in the series is **34**.

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