Write 7th term from the end of the AP: 7, 9, 11, 13,............213.

Answer

To find the 7th term from the end of the arithmetic progression (AP) given by the sequence 7, 9, 11, ..., 213, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the first term (a) and the common difference (d)**:
- The first term \( a = 7 \).
- The common difference \( d = 9 - 7 = 2 \).

2. **Identify the last term (l)**:
- The last term \( l = 213 \).

3. **Determine the number of terms (n) in the AP**:
- We can use the formula for the nth term of an AP, which is given by:
\[ T_n = a + (n-1)d \]
- Setting \( T_n = 213 \), we can solve for \( n \):
\[ 213 = 7 + (n-1) \cdot 2 \]
\[ 213 - 7 = (n-1) \cdot 2 \]
\[ 206 = (n-1) \cdot 2 \]
\[ n-1 = \frac{206}{2} = 103 \]
\[ n = 103 + 1 = 104 \]
- Thus, there are 104 terms in the AP.

4. **Find the 7th term from the end**:
- The 7th term from the end can be found using the formula:
\[ T_{n-6} = T_{104-6} = T_{98} \]
- Now, we can find \( T_{98} \):
\[ T_{98} = a + (98-1)d \]
\[ T_{98} = 7 + (97) \cdot 2 \]
\[ T_{98} = 7 + 194 = 201 \]

5. **Conclusion**:
- The 7th term from the end of the AP is \( 201 \).

### Final Answer:
The 7th term from the end of the AP is **201**.