The nth term of an A.P. is (5n-1). Find the sum of its 'n' terms.

Explanation

To find the sum of the first 'n' terms of the arithmetic progression (A.P.) whose nth term is given by \( a_n = 5n - 1 \), we can follow these steps:

### Step 1: Identify the first term (a)
The first term of the A.P. can be found by substituting \( n = 1 \) into the formula for the nth term.

\[ a_1 = 5(1) - 1 = 5 - 1 = 4 \]

### Step 2: Identify the last term (l)
The last term (nth term) can be found by substituting \( n \) into the formula for the nth term.

\[ l = a_n = 5n - 1 \]

### Step 3: Use the formula for the sum of n terms (S_n)
The sum of the first 'n' terms of an A.P. is given by the formula:

\[ S_n = \frac{n}{2} \times (a + l) \]

Substituting the values of \( a \) and \( l \):

\[ S_n = \frac{n}{2} \times (4 + (5n - 1)) \]

### Step 4: Simplify the expression
Now simplify the expression inside the parentheses:

\[ S_n = \frac{n}{2} \times (4 + 5n - 1) = \frac{n}{2} \times (5n + 3) \]

### Step 5: Final expression for the sum of n terms
Thus, the sum of the first 'n' terms of the A.P. is:

\[ S_n = \frac{n}{2} \times (5n + 3) \]

### Summary
The sum of the first 'n' terms of the A.P. is:

\[ S_n = \frac{n(5n + 3)}{2} \]

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