What value will come in place of question mark (?) in the questions given below?
`3, 10, 32, 111, 460, 2315, ? `

Options

A. 13903
B. 13904
C. 13902
D. 13908

Answer

To find the value that will come in place of the question mark (?) in the sequence `3, 10, 32, 111, 460, 2315, ?`, we need to identify the pattern in the sequence. Let's analyze the numbers step by step.

### Step 1: Identify the pattern
We start with the first number, which is 3.

- The second number is 10. We can express it as:
\[ 3 \times 1 + 7 = 10 \]

### Step 2: Continue the pattern
Now, let's find the third number, which is 32. We will use the second number (10) and apply a similar operation:
- The third number can be expressed as:
\[ 10 \times 3 + 2 = 32 \]

### Step 3: Find the fourth number
Next, we look for the fourth number, which is 111. We will use the third number (32):
- The fourth number can be expressed as:
\[ 32 \times 3 + 15 = 111 \]

### Step 4: Find the fifth number
Now, we will find the fifth number, which is 460. We will use the fourth number (111):
- The fifth number can be expressed as:
\[ 111 \times 4 + 16 = 460 \]

### Step 5: Find the sixth number
Next, we find the sixth number, which is 2315. We will use the fifth number (460):
- The sixth number can be expressed as:
\[ 460 \times 5 + 15 = 2315 \]

### Step 6: Find the seventh number
Now, we need to find the seventh number using the sixth number (2315):
- We will apply the same pattern:
\[ 2315 \times 6 + 12 = ? \]

Calculating this gives:
\[ 2315 \times 6 = 13890 \]
Adding 12:
\[ 13890 + 12 = 13902 \]

Thus, the value that will come in place of the question mark (?) is **13902**.

### Summary of Steps:
1. Identify the pattern using multiplication and addition.
2. Apply the identified pattern to find each subsequent number in the sequence.
3. Calculate the final value for the seventh term.