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
12 28 64 140
37 a b c d e
which of the following will come in place of ( e ) ?

Options

A. 1412
B. 164
C. 696
D. 78

Answer

To solve the problem, we need to analyze the given series and find the pattern to complete it. The series provided is:

12, 28, 64, 140

We also have a starting number:

37 a b c d e

We need to find the values of a, b, c, d, and e based on the pattern established in the first series.

### Step 1: Identify the Pattern in the First Series
Let's look at the differences between the consecutive terms in the series:

- From 12 to 28: \(28 - 12 = 16\)
- From 28 to 64: \(64 - 28 = 36\)
- From 64 to 140: \(140 - 64 = 76\)

Now, let's observe the differences:
- The difference between 12 and 28 is \(16\).
- The difference between 28 and 64 is \(36\).
- The difference between 64 and 140 is \(76\).

### Step 2: Analyzing the Differences
The differences themselves seem to follow a pattern:
- The difference between 16 and 36 is \(20\).
- The difference between 36 and 76 is \(40\).

This suggests that the differences are increasing by \(20\) each time.

### Step 3: Continuing the Pattern
Following this pattern, the next difference should be:
- \(76 + 60 = 136\)

### Step 4: Finding the Next Term
Now, we can find the next term after 140:
- \(140 + 136 = 276\)

### Step 5: Establishing the Next Sequence
Now we have the complete series:
12, 28, 64, 140, 276

### Step 6: Applying the Pattern to the New Series
Now we apply the same pattern starting from 37:
1. **For a**:
- \(37 \times 2 + 4 = 74 + 4 = 78\)

2. **For b**:
- \(78 \times 2 + 8 = 156 + 8 = 164\)

3. **For c**:
- \(164 \times 2 + 12 = 328 + 12 = 340\)

4. **For d**:
- \(340 \times 2 + 16 = 680 + 16 = 696\)

5. **For e**:
- \(696 \times 2 + 20 = 1392 + 20 = 1412\)

### Final Result
Thus, the value of \(e\) is **1412**.

### Summary of Steps:
1. Identify the differences in the first series.
2. Determine the pattern of differences.
3. Calculate the next term in the first series.
4. Apply the same pattern to the new starting number (37).
5. Calculate each subsequent term until reaching \(e\).