What will come in place of question mark (?) in the following sereis questions?
1,3,9,31,129,?

Options

A. 661
B. 671
C. 651
D. 641

Answer

To solve the series: 1, 3, 9, 31, 129, ?, we need to identify the pattern in the series. Let's break it down step by step.

### Step 1: Identify the pattern
We start with the given series:
1, 3, 9, 31, 129.

### Step 2: Analyze the differences
Let's look at how each term is derived from the previous term:
- From 1 to 3:
- \(1 \times 2 + 1 = 3\)
- From 3 to 9:
- \(3 \times 2 + 3 = 9\)
- From 9 to 31:
- \(9 \times 3 + 4 = 31\)
- From 31 to 129:
- \(31 \times 4 + 5 = 129\)

### Step 3: Establish the formula
From our observations, we can see a pattern:
- The first term is multiplied by 2 and then added to 1.
- The second term is multiplied by 2 and then added to 3.
- The third term is multiplied by 3 and then added to 4.
- The fourth term is multiplied by 4 and then added to 5.

### Step 4: Apply the pattern to find the next term
Now, we need to find the next term after 129:
- The next term will be derived from 129:
- \(129 \times 5 + 6\)

### Step 5: Calculate the next term
Now, we perform the calculation:
- \(129 \times 5 = 645\)
- \(645 + 6 = 651\)

Thus, the next term in the series is **651**.

### Final Answer
The number that will come in place of the question mark (?) is **651**.

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