In the following A.P. 's find the missing terms in the boxes :
`5, square,square, 9 (1)/(2)`

Answer

To find the missing terms in the arithmetic progression (A.P.) given as `5, square, square, 9.5`, we will follow these steps:

### Step 1: Identify the first term and the last term
The first term \( A \) is given as \( 5 \) and the last term is \( 9.5 \) (which is \( 9 \frac{1}{2} \) in fractional form).

### Step 2: Set up the formula for the A.P.
In an A.P., the \( n^{th} \) term can be expressed as:
\[ T_n = A + (n-1)D \]
where \( D \) is the common difference.

### Step 3: Identify the position of the last term
The last term \( 9.5 \) is the 4th term in this sequence. Thus, we can write:
\[ T_4 = A + 3D \]
Substituting the known values:
\[ 9.5 = 5 + 3D \]

### Step 4: Solve for \( D \)
Rearranging the equation:
\[ 3D = 9.5 - 5 \]
\[ 3D = 4.5 \]
Now, divide both sides by 3:
\[ D = \frac{4.5}{3} = 1.5 \]

### Step 5: Find the missing terms
Now that we have \( D = 1.5 \), we can find the missing terms.

1. The second term (\( T_2 \)):
\[ T_2 = A + D = 5 + 1.5 = 6.5 \]

2. The third term (\( T_3 \)):
\[ T_3 = A + 2D = 5 + 2 \times 1.5 = 5 + 3 = 8 \]

### Final Answer
The missing terms in the A.P. are:
- Second term: \( 6.5 \)
- Third term: \( 8 \)

Thus, the complete A.P. is:
\[ 5, 6.5, 8, 9.5 \]