What is value of `a_(16)` for the A.P. `-10, -12, -14, -16`………….

Answer

To find the value of \( a_{16} \) for the given arithmetic progression (A.P.) \(-10, -12, -14, -16, \ldots\), we will follow these steps:

### Step 1: Identify the first term and common difference
The first term \( a \) of the A.P. is the first number in the sequence:
\[ a = -10 \]

Next, we need to find the common difference \( d \). The common difference is calculated by subtracting the first term from the second term:
\[ d = -12 - (-10) = -12 + 10 = -2 \]

### Step 2: Use the formula for the \( n \)-th term of an A.P.
The formula for the \( n \)-th term \( a_n \) of an arithmetic progression is given by:
\[ a_n = a + (n - 1) \cdot d \]

### Step 3: Substitute \( n = 16 \) into the formula
We want to find \( a_{16} \):
\[ a_{16} = a + (16 - 1) \cdot d \]
Substituting the values of \( a \) and \( d \):
\[ a_{16} = -10 + (15) \cdot (-2) \]

### Step 4: Calculate the value
Now we perform the calculation:
\[ a_{16} = -10 + (-30) = -10 - 30 = -40 \]

### Final Answer
Thus, the value of \( a_{16} \) is:
\[ \boxed{-40} \]