Write the next two terms of the A.P. : 3, -1, -5, ... .

Answer

To find the next two terms of the arithmetic progression (A.P.) given as 3, -1, -5, we can follow these steps:

### Step 1: Identify the first term (a) and the common difference (d).
- The first term \( a \) is 3.
- To find the common difference \( d \), we subtract the first term from the second term:
\[ d = -1 - 3 = -4 \]

### Step 2: Use the formula for the nth term of an A.P.
The formula for the nth term of an A.P. is given by:
\[ a_n = a + (n - 1)d \]
where \( a \) is the first term, \( d \) is the common difference, and \( n \) is the term number.

### Step 3: Find the fourth term (a₄).
- Substitute \( n = 4 \) into the formula:
\[ a_4 = a + (4 - 1)d = 3 + 3(-4) \]
- Calculate:
\[ a_4 = 3 + (-12) = 3 - 12 = -9 \]

### Step 4: Find the fifth term (a₅).
- Substitute \( n = 5 \) into the formula:
\[ a_5 = a + (5 - 1)d = 3 + 4(-4) \]
- Calculate:
\[ a_5 = 3 + (-16) = 3 - 16 = -13 \]

### Conclusion
The next two terms of the A.P. are:
- Fourth term: -9
- Fifth term: -13

Thus, the next two terms of the A.P. are **-9** and **-13**.

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