Find the next term of the following patterns
107, 97, 82, 62,….

Options

A. 52
B. 42
C. 37
D. 47

Answer

To find the next term in the sequence 107, 97, 82, 62, we can follow these steps:

### Step 1: Identify the differences between consecutive terms
- The difference between 107 and 97 is:
\[ 107 - 97 = 10 \]
- The difference between 97 and 82 is:
\[ 97 - 82 = 15 \]
- The difference between 82 and 62 is:
\[ 82 - 62 = 20 \]

### Step 2: Analyze the pattern of differences
Now we have the differences:
- First difference: 10
- Second difference: 15
- Third difference: 20

We can see that the differences themselves are increasing by 5 each time:
- From 10 to 15, the increase is 5.
- From 15 to 20, the increase is also 5.

### Step 3: Predict the next difference
Following the pattern, the next difference should be:
\[ 20 + 5 = 25 \]

### Step 4: Subtract the next difference from the last term
Now, we subtract this next difference from the last term in the sequence (62):
\[ 62 - 25 = 37 \]

### Conclusion
Thus, the next term in the sequence is:
\[ \boxed{37} \]

---