What value will come in place of question mark (?) in the number series given below ?
`"2156 2077 ? 1682 1366"`

Options

A. 1919
B. 1829
C. 2022
D. 1661

Answer

To find the value that will come in place of the question mark (?) in the number series `2156, 2077, ?, 1682, 1366`, we can follow these steps:

### Step 1: Identify the differences between the numbers
We will start by calculating the differences between consecutive terms in the series.

1. The difference between the first term (2156) and the second term (2077):
\[ 2156 - 2077 = 79 \]

2. The difference between the second term (2077) and the unknown term (let's call it \(X\)):
\[ 2077 - X \]

3. The difference between the unknown term \(X\) and the fourth term (1682):
\[ X - 1682 \]

4. The difference between the fourth term (1682) and the fifth term (1366):
\[ 1682 - 1366 = 316 \]

### Step 2: Establish a pattern in the differences
From our calculations, we see that:
- The difference between the first and second terms is 79.
- The difference between the fourth and fifth terms is 316.

Notice that \(316\) can be expressed as \(79 \times 4\). This suggests that the differences might follow a pattern based on multiples of \(79\).

### Step 3: Set up the equations based on the pattern
We can assume the differences follow the pattern:
- First difference: \(79 \times 1\)
- Second difference: \(79 \times 2\)
- Third difference: \(79 \times 3\)
- Fourth difference: \(79 \times 4\)

Thus, we can write:
1. \(2077 - 2156 = -79\) (which is \(79 \times 1\))
2. \(X - 2077 = -79 \times 2\)
3. \(1682 - X = -79 \times 3\)
4. \(1366 - 1682 = -79 \times 4\)

### Step 4: Solve for \(X\)
Using the second difference:
\[ X = 2077 - 79 \times 2 \]
Calculating \(79 \times 2\):
\[ 79 \times 2 = 158 \]
Now substituting back:
\[ X = 2077 - 158 = 1919 \]

### Step 5: Verify the value of \(X\)
Now, we will verify by checking the difference between \(X\) and the next term:
\[ 1682 - 1919 = -237 \]
Calculating \(79 \times 3\):
\[ 79 \times 3 = 237 \]
This confirms that the difference is correct.

### Final Answer
Thus, the value that comes in place of the question mark (?) is:
\[ \boxed{1919} \]