Find the value of (?) in the following number series.
`1.5," "3," "12,72," "576," "?`

Options

A. A)5480
B. B)5620
C. C)5580
D. D)5760

Answer

To find the value of (?) in the number series: 1.5, 3, 12, 72, 576, ?, we will analyze the pattern in the series step by step.

### Step 1: Identify the Pattern
We will look at how each term relates to the previous term.

- The first term is **1.5**.
- The second term is **3**.
- Here, \( 1.5 \times 2 = 3 \).

- The third term is **12**.
- Here, \( 3 \times 4 = 12 \).

- The fourth term is **72**.
- Here, \( 12 \times 6 = 72 \).

- The fifth term is **576**.
- Here, \( 72 \times 8 = 576 \).

### Step 2: Establish the Multiplication Pattern
From the above calculations, we can see that:
- The first multiplication is by **2**.
- The second multiplication is by **4**.
- The third multiplication is by **6**.
- The fourth multiplication is by **8**.

The pattern in the multipliers is: **2, 4, 6, 8**.

### Step 3: Determine the Next Multiplier
Following the established pattern, the next multiplier should be **10** (continuing the even number sequence).

### Step 4: Calculate the Missing Term
Now, we will use this multiplier to find the missing term (denoted as K):
- \( K = 576 \times 10 \)

Calculating this gives:
- \( K = 5760 \)

### Conclusion
Thus, the value of (?) in the series is **5760**.