Find the nth term of the A.P. `-10, -15, -20, -25`…………..

Answer

To find the nth term of the arithmetic progression (A.P.) given by the series `-10, -15, -20, -25`, we can follow these steps:

### Step 1: Identify the first term (A)
The first term of the A.P. is the first number in the series.
- **A = -10**

### Step 2: Determine the common difference (D)
The common difference (D) can be calculated by subtracting the first term from the second term or the second term from the third term, and so on.
- **D = Second term - First term = -15 - (-10) = -15 + 10 = -5**

### Step 3: Write the formula for the nth term
The formula for the nth term (A_n) of an A.P. is given by:
\[ A_n = A + (n - 1)D \]

### Step 4: Substitute the values of A and D into the formula
Now we substitute A and D into the formula:
\[ A_n = -10 + (n - 1)(-5) \]

### Step 5: Simplify the expression
Now we simplify the expression:
\[ A_n = -10 - 5(n - 1) \]
\[ A_n = -10 - 5n + 5 \]
\[ A_n = -5 - 5n \]

### Final Result
Thus, the nth term of the A.P. is:
\[ A_n = -5 - 5n \]

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