The sum of the first n terms of a series is 31, and the sum of the first `n - 1` terms of the series is 20. What is the value of nth terms in the series?

Options

A. 9
B. 11
C. 20
D. 31

Answer

To find the value of the nth term in the series, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The sum of the first n terms of the series, denoted as \( S_n \), is given as 31.
- The sum of the first \( n - 1 \) terms of the series, denoted as \( S_{n-1} \), is given as 20.

2. **Write the Relationship Between the Sums**:
- The nth term of the series, denoted as \( a_n \), can be expressed using the relationship between the sums:
\[ a_n = S_n - S_{n-1} \]

3. **Substitute the Given Values**:
- Substitute the values of \( S_n \) and \( S_{n-1} \) into the equation:
\[ a_n = 31 - 20 \]

4. **Calculate the nth Term**:
- Perform the subtraction:
\[ a_n = 11 \]

5. **Conclusion**:
- Therefore, the value of the nth term in the series is:
\[ a_n = 11 \]

### Summary of the Steps:
- We used the relationship between the sums of the series to isolate the nth term.
- By substituting the known values, we calculated the nth term.