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
2 3 8 27
5 a b c d e
which of the following will come in place of ( e ) ?

Options

A. 184
B. 6
C. 925
D. 45

Answer

To solve the given problem, we need to identify the pattern in the series provided and then continue that pattern starting from the number given (5).

The original series is:
2, 3, 8, 27

Let's analyze the series step by step:

1. **Identify the pattern in the original series:**
- The first term is \(2\).
- The second term is \(3\).
- The third term is \(8\).
- The fourth term is \(27\).

Observing the terms, we can see that:
- \(2 = 2^1\)
- \(3 = 3^1\)
- \(8 = 2^3\)
- \(27 = 3^3\)

The series seems to alternate between powers of 2 and powers of 3.

2. **Continuing the pattern:**
- The next term after \(27\) should follow the pattern of alternating powers. The next term should be \(2^4\) since the last term \(27\) (which is \(3^3\)) was a power of 3.
- Therefore, the next term is \(2^4 = 16\).

3. **Continuing further:**
- The term after \(16\) should be \(3^4\).
- Therefore, the next term is \(3^4 = 81\).

4. **So far, we have:**
- The series now looks like: \(2, 3, 8, 27, 16, 81\).

5. **Now, we need to fill in the series starting from the number given (5):**
- The series we need to complete is: \(5, a, b, c, d, e\).
- Following the established pattern, we will continue from \(5\) (which is not part of the original series but will follow the same pattern):
- The next term after \(5\) will be \(2^1 = 2\) (but since we are starting from \(5\), we will just continue the pattern).
- The next term should be \(3^1 = 3\).
- The next term should be \(2^3 = 8\).
- The next term should be \(3^3 = 27\).
- The next term should be \(2^4 = 16\).
- The next term should be \(3^4 = 81\).

6. **Final series starting from 5:**
- Thus, the completed series is: \(5, 6, 8, 27, 16, 81\).

7. **Identifying the value of \(e\):**
- The value of \(e\) will be the last term we calculated, which is \(81\).

**Final Answer:**
The value of \(e\) is \(81\).

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