If the `n^(th)` term of an A.P is `(5n-2)` ,find its `19^(th) term`

Answer

To find the 19th term of the arithmetic progression (A.P) where the nth term is given by the formula \( T_n = 5n - 2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the nth term formula**:
The nth term of the A.P is given as \( T_n = 5n - 2 \).

2. **Substitute n with 19**:
To find the 19th term, we substitute \( n \) with 19 in the formula:
\[ T_{19} = 5(19) - 2 \]

3. **Calculate \( 5 \times 19 \)**:
First, calculate \( 5 \times 19 \):
\[ 5 \times 19 = 95 \]

4. **Subtract 2 from 95**:
Now, subtract 2 from 95:
\[ T_{19} = 95 - 2 = 93 \]

5. **Conclusion**:
Therefore, the 19th term of the A.P is:
\[ T_{19} = 93 \]

### Final Answer:
The 19th term of the arithmetic progression is **93**.

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