10th term of the A.P. `-0,1, -0.2, -0.3,………` is

Options

A. `-0.9`
B. `-0.8`
C. `-1.0`
D. `-1.1`

Answer

To find the 10th term of the arithmetic progression (A.P.) given as `-0.1, -0.2, -0.3, ...`, we will follow these steps:

### Step 1: Identify the first term (a) and the common difference (d)
- The first term \( a \) of the A.P. is \( -0.1 \).
- The common difference \( d \) can be calculated as:
\[ d = \text{second term} - \text{first term} = -0.2 - (-0.1) = -0.2 + 0.1 = -0.1 \]

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

### Step 3: Substitute the values into the formula
We need to find the 10th term, so we set \( n = 10 \):
\[ T_{10} = a + (10 - 1) \cdot d \]
Substituting the values of \( a \) and \( d \):
\[ T_{10} = -0.1 + (10 - 1) \cdot (-0.1) \]

### Step 4: Simplify the expression
Calculating the expression:
\[ T_{10} = -0.1 + 9 \cdot (-0.1) \]
\[ T_{10} = -0.1 - 0.9 \]
\[ T_{10} = -1.0 \]

### Final Answer
The 10th term of the A.P. is \( -1.0 \).

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