2, 17, 89, 359, 1079, ?

Options

A. 2158
B. 2159
C. 1869
D. 1969

Explanation

To find the missing number in the series: 2, 17, 89, 359, 1079, ?, we will analyze the pattern in the series step by step.

### Step 1: Identify the pattern between the numbers.
Let's look at how each number relates to the next one in the series.

1. From 2 to 17:
- We can multiply 2 by 9 and subtract 1:
\[ 2 \times 9 - 1 = 18 - 1 = 17 \]

2. From 17 to 89:
- We can multiply 17 by 5 and add 4:
\[ 17 \times 5 + 4 = 85 + 4 = 89 \]

3. From 89 to 359:
- We can multiply 89 by 4 and add 3:
\[ 89 \times 4 + 3 = 356 + 3 = 359 \]

4. From 359 to 1079:
- We can multiply 359 by 3 and add 2:
\[ 359 \times 3 + 2 = 1077 + 2 = 1079 \]

### Step 2: Establish the next operation.
Now we need to find the next number after 1079. Following the pattern, we see that we are multiplying by decreasing integers (9, 5, 4, 3) and adding decreasing integers (4, 3, 2).

Following this pattern, the next operation should involve multiplying by 2 and adding 1:
\[ 1079 \times 2 + 1 \]

### Step 3: Calculate the next number.
Now let's perform the calculation:
\[ 1079 \times 2 = 2158 \]
Now add 1:
\[ 2158 + 1 = 2159 \]

### Conclusion:
The missing number in the series is **2159**.

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