`14,25,55,140,` ? Options are (a) 386 (b) 388 (c) 398 (d) None of the above.

Options

A. 386
B. 388
C. 398
D. None of the above

Answer

To solve the series: 14, 25, 55, 140, ?, we will analyze the pattern in the series step by step.

### Step 1: Identify the first term
The first term is **14**.

### Step 2: Identify the second term
The second term is **25**. To find how we got from 14 to 25, we can express it as:
\[ 25 = 14 + (3^1 + 2) \]
Where \(3^1 = 3\). So, \(14 + 3 + 2 = 25\).

### Step 3: Identify the third term
The third term is **55**. To find how we got from 25 to 55:
\[ 55 = 25 + (3^3 + 3) \]
Where \(3^3 = 27\). So, \(25 + 27 + 3 = 55\).

### Step 4: Identify the fourth term
The fourth term is **140**. To find how we got from 55 to 140:
\[ 140 = 55 + (3^4 + 4) \]
Where \(3^4 = 81\). So, \(55 + 81 + 4 = 140\).

### Step 5: Identify the next term
Now, we need to find the next term after 140. Following the established pattern:
\[ ? = 140 + (3^5 + 5) \]
Where \(3^5 = 243\). So, we calculate:
\[ 140 + 243 + 5 = 388 \]

### Conclusion
Thus, the next term in the series is **388**.

### Final Answer
The answer is **388** (Option b).

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