In each of the following question a number series is a given. After the series, 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 given questions.
2 4 9 20 43 90
3 (a) (b) (c) (d) (e)
Which of the following numbers will cone in place of (d) ?

Options

A. 58
B. 99
C. 48
D. 59

Answer

To solve the problem, we need to identify the pattern in the given series and then apply that pattern to the starting number, which is 3, to find the subsequent numbers in the series.

### Given Series:
2, 4, 9, 20, 43, 90

### Step 1: Identify the Pattern
Let's analyze the given series:

1. From 2 to 4:
- \(2 \times 2 + 0 = 4\)

2. From 4 to 9:
- \(4 \times 2 + 1 = 9\)

3. From 9 to 20:
- \(9 \times 2 + 2 = 20\)

4. From 20 to 43:
- \(20 \times 2 + 3 = 43\)

5. From 43 to 90:
- \(43 \times 2 + 4 = 90\)

From this, we can see that the pattern involves multiplying the previous number by 2 and then adding an incrementing integer (0, 1, 2, 3, 4).

### Step 2: Apply the Pattern to the Starting Number (3)
Now, we will apply the same pattern starting from the number 3:

1. First term (given):
- \(3\)

2. Second term (a):
- \(3 \times 2 + 0 = 6\)

3. Third term (b):
- \(6 \times 2 + 1 = 13\)

4. Fourth term (c):
- \(13 \times 2 + 2 = 28\)

5. Fifth term (d):
- \(28 \times 2 + 3 = 59\)

6. Sixth term (e):
- \(59 \times 2 + 4 = 122\)

### Conclusion
Thus, the value that will come in place of (d) is **59**.