In each of the following question a number series is given .After the series is given.After the series below it a number is given followed by a,b,c,d and e , you have to complete the series starting with the number given following the sequence of the given series. Then answer the question given below it
5 12 60 340
7a b c d e
which of the following will come in place of ( e ) ?

Options

A. 172
B. 3222
C. 1012
D. 20164

Answer

To solve the problem, we need to identify the pattern in the given series and then apply it to find the missing term (e) in the new series starting with 7.

### Step-by-step Solution:

1. **Identify the pattern in the original series:**
- The given series is 5, 12, 60, 340.
- Let's analyze the differences between the terms:
- From 5 to 12: \( 12 - 5 = 7 \)
- From 12 to 60: \( 60 - 12 = 48 \)
- From 60 to 340: \( 340 - 60 = 280 \)

2. **Look for a multiplication pattern:**
- Instead of just looking at the differences, let's see if there's a multiplication pattern:
- \( 5 \times 2 + 2 = 12 \)
- \( 12 \times 5 = 60 \)
- \( 60 \times 5 + 40 = 340 \)

3. **Establish a consistent pattern:**
- The multipliers seem to be increasing:
- First, we multiply by 2, then by 5, and then by 5 again, with an additional increment.
- We can summarize the pattern as follows:
- \( a_1 = 5 \)
- \( a_2 = a_1 \times 2 + 2 = 12 \)
- \( a_3 = a_2 \times 5 = 60 \)
- \( a_4 = a_3 \times 5 + 40 = 340 \)

4. **Apply the pattern to the new series starting with 7:**
- Now we need to find the terms starting from 7:
- \( b = 7 \times 2 + 2 = 16 \)
- \( c = 16 \times 5 = 80 \)
- \( d = 80 \times 5 + 40 = 440 \)
- \( e = 440 \times 5 + 40 = 2200 \)

5. **Final answer:**
- The value of (e) is **2200**.