Find the wrong number in the following number series.
8,10,20,70,320,1570,7830

Options

A. 7820
B. 10
C. 8
D. 320

Answer

To find the wrong number in the series: 8, 10, 20, 70, 320, 1570, 7830, we will analyze the pattern in the differences between consecutive terms.

### Step-by-Step Solution:

1. **Identify the Series**: The given series is:
\[ 8, 10, 20, 70, 320, 1570, 7830 \]

2. **Calculate the Differences**:
- The difference between the first two terms: \(10 - 8 = 2\)
- The difference between the second and third terms: \(20 - 10 = 10\)
- The difference between the third and fourth terms: \(70 - 20 = 50\)
- The difference between the fourth and fifth terms: \(320 - 70 = 250\)
- The difference between the fifth and sixth terms: \(1570 - 320 = 1250\)
- The difference between the sixth and seventh terms: \(7830 - 1570 = 6260\)

So, the differences are:
\[ 2, 10, 50, 250, 1250, 6260 \]

3. **Identify the Pattern in Differences**:
- Notice that each difference seems to be multiplied by 5 to get the next difference:
- \(2 \times 5 = 10\)
- \(10 \times 5 = 50\)
- \(50 \times 5 = 250\)
- \(250 \times 5 = 1250\)
- \(1250 \times 5 = 6250\) (but we have \(6260\) instead)

4. **Find the Incorrect Term**:
- The last difference should have been \(6250\) instead of \(6260\).
- If we subtract the correct difference from the last term:
\[ 1570 + 6250 = 7820 \]
- The series should have been:
\[ 8, 10, 20, 70, 320, 1570, 7820 \]
- Therefore, the incorrect term in the series is \(7830\).

5. **Conclusion**:
- The wrong number in the series is **7830**. It should be **7820**.