In each of the following questions, a number series is given after the series, below it a number is given followed by (a) (b) (c) (d). You have to complete the series starting with the number given following the squence of the given series.
4 21 120 595 2376 7125
7 (a) (b) (c) (d) (e)
Which of the following number will come in place of (c) ?

Options

A. 1775
B. 1725
C. 1230
D. 1225

Answer

To solve the problem, we need to identify the pattern in the given number series: 4, 21, 120, 595, 2376, 7125. We will then apply this pattern starting from the number 7 to find the value that will replace (c).

### Step-by-Step Solution:

1. **Identify the Pattern in the Series:**
- The series is: 4, 21, 120, 595, 2376, 7125.
- We can observe that each number seems to be derived from the previous number by a specific multiplication and subtraction.

2. **Calculate the Multiplication Factor and Subtraction:**
- From 4 to 21:
- \(4 \times 7 - 1 = 28 - 7 = 21\)
- From 21 to 120:
- \(21 \times 6 - 6 = 126 - 6 = 120\)
- From 120 to 595:
- \(120 \times 5 - 5 = 600 - 5 = 595\)
- From 595 to 2376:
- \(595 \times 4 - 4 = 2380 - 4 = 2376\)
- From 2376 to 7125:
- \(2376 \times 3 - 3 = 7128 - 3 = 7125\)

The pattern shows that the multiplication factor decreases by 1 each time, and the subtraction matches the multiplication factor.

3. **Apply the Pattern Starting from 7:**
- Now we need to apply this pattern starting from the number 7.
- First, we will multiply by 7 and subtract 1:
- \(7 \times 7 - 1 = 49 - 1 = 48\) (This is the first term)
- Next, we multiply by 6 and subtract 6:
- \(48 \times 6 - 6 = 288 - 6 = 282\) (This is the second term)
- Next, we multiply by 5 and subtract 5:
- \(282 \times 5 - 5 = 1410 - 5 = 1405\) (This is the third term, which corresponds to (c))

4. **Final Answer:**
- The number that will come in place of (c) is **1405**.