Find the value of (?) in the following number series.
`163," "?," "43," "23," "13," "8`

Options

A. A)92
B. B)83
C. C)78
D. D)54

Answer

To find the value of (?) in the number series `163, "?", 43, 23, 13, 8`, we will analyze the pattern of the series step by step.

### Step 1: Identify the Series
The given series is:
- 1st term: 163
- 2nd term: ?
- 3rd term: 43
- 4th term: 23
- 5th term: 13
- 6th term: 8

### Step 2: Analyze the Differences
Let's look at the differences between the consecutive terms starting from the last known term (8) and moving backward:

- From 8 to 13: \( 13 - 8 = 5 \)
- From 13 to 23: \( 23 - 13 = 10 \)
- From 23 to 43: \( 43 - 23 = 20 \)

### Step 3: Identify the Pattern in Differences
The differences we calculated are:
- 5 (from 8 to 13)
- 10 (from 13 to 23)
- 20 (from 23 to 43)

We can see that the differences are increasing:
- The first difference is 5.
- The second difference is double the first: \( 5 \times 2 = 10 \).
- The third difference is double the second: \( 10 \times 2 = 20 \).

### Step 4: Predict the Next Difference
Following the established pattern, the next difference should be double the last difference:
- Next difference: \( 20 \times 2 = 40 \).

### Step 5: Calculate the Missing Term
Now, we can find the missing term (the second term) by subtracting this next difference from the third term (43):
- \( ? = 43 - 40 = 3 \).

### Step 6: Verify the Series
To ensure the series remains consistent, we can check the differences moving forward:
- From 3 to 43: \( 43 - 3 = 40 \)
- From 43 to 163: \( 163 - 3 = 160 \)

The differences from 8 to 13, 13 to 23, 23 to 43, and 43 to 163 are:
- 5, 10, 20, and 40, which confirms our pattern.

### Final Answer
Thus, the value of (?) is **3**.

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