A series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series:
a a_a_ca_ c d a _ c_ e

Options

A. (a) b b b b d
B. (b) b b c a d
C. (c) c a d b d
D. (d) a b d a c

Explanation

To solve the problem of completing the series given as: a a_a_ca_ c d a _ c_ e, we need to identify the pattern in the series and fill in the missing letters.

### Step-by-Step Solution:

1. **Identify the existing letters in the series**:
The series is: a a _ a c _ c d a _ c _ e.
The letters present are: a, c, d, e.

2. **Count the occurrences of each letter**:
- 'a' appears 5 times.
- 'c' appears 3 times.
- 'd' appears 1 time.
- 'e' appears 1 time.

3. **Look for patterns**:
- The series starts with 'a' and has a repetition of 'a' and 'c'.
- After 'd', 'a' appears again, followed by another 'c' and then 'e'.

4. **Fill in the first blank**:
- The first blank is after 'a a', and since 'a' is repeated, it is logical to fill this blank with 'b' (the next letter in the sequence).
- So, the series now looks like: a a b a c _ c d a _ c _ e.

5. **Fill in the second blank**:
- The second blank is after 'c'. Following the pattern, we can fill this blank with 'b' again.
- The series now looks like: a a b a c b c d a _ c _ e.

6. **Fill in the third blank**:
- The third blank is after 'a'. Following the pattern, we can fill this blank with 'b'.
- The series now looks like: a a b a c b c d a b c _ e.

7. **Fill in the fourth blank**:
- The fourth blank is before 'e'. To maintain the pattern, we can fill this blank with 'd'.
- The final series now looks like: a a b a c b c d a b c d e.

8. **Check the completed series**:
- The completed series is: a a b a c b c d a b c d e.
- This series follows a logical pattern of introducing 'b', 'c', and 'd' after 'a' has been established.

### Conclusion:
The correct alternative that completes the series is: **BBBD**.