What will come in place of question mark(?) in the given number series.
4 14 24 39 69 ?

Options

A. 152
B. 164
C. 184
D. 144

Answer

To solve the given number series: 4, 14, 24, 39, 69, ?, we need to identify the pattern in the differences between the consecutive numbers.

**Step 1: Calculate the differences between consecutive terms.**
- Difference between 14 and 4:
\( 14 - 4 = 10 \)
- Difference between 24 and 14:
\( 24 - 14 = 10 \)
- Difference between 39 and 24:
\( 39 - 24 = 15 \)
- Difference between 69 and 39:
\( 69 - 39 = 30 \)

So, the differences are:
10, 10, 15, 30.

**Step 2: Analyze the differences.**
- The first two differences are both 10.
- The third difference is 15, which can be seen as \( 10 + 5 \).
- The fourth difference is 30, which can be seen as \( 15 + 15 \).

The pattern seems to be that we are adding increasing multiples of 5 to the previous difference.

**Step 3: Determine the next difference.**
- The next difference should be \( 30 + 45 \) (as we are increasing by 15, which is \( 5 \times 3 \)).
- So, the next difference is \( 30 + 45 = 75 \).

**Step 4: Calculate the next term in the series.**
- To find the term that comes after 69, we add the next difference (75) to 69:
\( 69 + 75 = 144 \).

Thus, the number that comes in place of the question mark (?) is **144**.

**Final Answer: 144**

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