What should come in place of the question mark (?) in the following number series ?
`820" "832" "808" "844" "796" "?`

Options

A. 866
B. 856
C. 586
D. 685

Answer

To find the missing number in the series: 820, 832, 808, 844, 796, ?, we will analyze the pattern of the series step by step.

### Step 1: Identify the differences between consecutive numbers
- From 820 to 832:
\[ 832 - 820 = 12 \]
- From 832 to 808:
\[ 808 - 832 = -24 \]
- From 808 to 844:
\[ 844 - 808 = 36 \]
- From 844 to 796:
\[ 796 - 844 = -48 \]

### Step 2: List the differences
Now we have the differences:
- \( +12 \)
- \( -24 \)
- \( +36 \)
- \( -48 \)

### Step 3: Identify the pattern in the differences
The differences alternate between positive and negative values, and they seem to increase in absolute value:
- The positive differences: \( 12, 36 \) (which can be seen as \( 12 \times 1 \) and \( 12 \times 3 \))
- The negative differences: \( -24, -48 \) (which can be seen as \( -12 \times 2 \) and \( -12 \times 4 \))

### Step 4: Predict the next difference
Following the established pattern, the next difference should be positive and increase by 12:
- The next positive difference should be \( +60 \) (which is \( 12 \times 5 \)).

### Step 5: Calculate the missing number
Now, we will add this difference to the last number in the series:
\[ 796 + 60 = 856 \]

### Conclusion
The number that should come in place of the question mark (?) is **856**.