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

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

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To find the first term of the arithmetic progression (A.P) where the nth term is given by the formula \( T_n = 5n - 2 \), we follow these steps: ### Step-by-Step Solution: 1. **Understand the nth term formula**: The nth term of an A.P is given as \( T_n = 5n - 2 \). Here, \( n \) represents the position of the term in the sequence. 2. **Identify the first term**: To find the first term of the A.P, we need to substitute \( n = 1 \) into the formula. The first term is denoted as \( T_1 \). 3. **Substitute \( n = 1 \)**: \[ T_1 = 5(1) - 2 \] 4. **Calculate \( T_1 \)**: \[ T_1 = 5 - 2 = 3 \] 5. **Conclusion**: The first term of the A.P is \( 3 \). ### Final Answer: The first term of the A.P is \( 3 \). ---
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