Find the missing number in the following series. 7, 10, 14, ?, 25, 32

Options

A. 18
B. 19
C. 20
D. 15

Answer

To find the missing number in the series 7, 10, 14, ?, 25, 32, we can follow these steps:

### Step 1: Identify the pattern in the series
We notice that the numbers are increasing. To understand how they are increasing, we should look at the differences between consecutive terms.

### Step 2: Calculate the differences between consecutive terms
- From 7 to 10:
\[ 10 - 7 = 3 \]
- From 10 to 14:
\[ 14 - 10 = 4 \]
- From 14 to the missing number (let's call it \( x \)):
\[ x - 14 \]
- From \( x \) to 25:
\[ 25 - x \]
- From 25 to 32:
\[ 32 - 25 = 7 \]

### Step 3: Establish the pattern of differences
The differences we have so far are:
- 3 (from 7 to 10)
- 4 (from 10 to 14)
- \( x - 14 \) (from 14 to \( x \))
- \( 25 - x \) (from \( x \) to 25)
- 7 (from 25 to 32)

We can see a pattern emerging in the differences: they are increasing by 1 each time:
- 3, 4, 5, 6, 7...

### Step 4: Determine the missing difference
Following the established pattern, the difference from 14 to \( x \) should be 5:
\[ x - 14 = 5 \]
Thus, we can solve for \( x \):
\[ x = 14 + 5 = 19 \]

### Step 5: Verify the next difference
Now, we check the difference from \( x \) (which is 19) to 25:
\[ 25 - 19 = 6 \]
This matches our expected difference of 6 in the pattern.

### Conclusion
The missing number in the series is:
\[ \boxed{19} \]

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