In the following A.P. 's find the missing terms in the boxes :
`-4, square, square, square,square , 6`

Answer

To find the missing terms in the arithmetic progression (A.P.) given as `-4, square, square, square, square, 6`, we will follow these steps:

### Step 1: Identify the first term and the last term
The first term (A1) is given as:
\[ A_1 = -4 \]
The last term (A6) is given as:
\[ A_6 = 6 \]

### 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:
\[ A_n = A + (n - 1) \cdot D \]
where \( A \) is the first term, \( D \) is the common difference, and \( n \) is the term number.

### Step 3: Set up the equation for the last term
For the 6th term:
\[ A_6 = A_1 + (6 - 1) \cdot D \]
Substituting the known values:
\[ 6 = -4 + 5D \]

### Step 4: Solve for D
Rearranging the equation to find \( D \):
\[ 5D = 6 + 4 \]
\[ 5D = 10 \]
\[ D = \frac{10}{5} = 2 \]

### Step 5: Find the missing terms
Now that we have the common difference \( D = 2 \), we can find the missing terms (A2, A3, A4, A5).

1. **A2**:
\[ A_2 = A_1 + D = -4 + 2 = -2 \]

2. **A3**:
\[ A_3 = A_1 + 2D = -4 + 2 \cdot 2 = -4 + 4 = 0 \]

3. **A4**:
\[ A_4 = A_1 + 3D = -4 + 3 \cdot 2 = -4 + 6 = 2 \]

4. **A5**:
\[ A_5 = A_1 + 4D = -4 + 4 \cdot 2 = -4 + 8 = 4 \]

### Step 6: Write the complete A.P.
Now, we can write the complete A.P.:
\[ -4, -2, 0, 2, 4, 6 \]

### Final Answer
The missing terms in the boxes are:
- A2: -2
- A3: 0
- A4: 2
- A5: 4

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