14th term of an `0.6, 1.7, 2.8, 3.9`, …… is :

Options

A. 14.9
B. `16.0`
C. `17.1`
D. `18.2`

Answer

To find the 14th term of the arithmetic progression (AP) given by the sequence 0.6, 1.7, 2.8, 3.9, we will follow these steps:

### Step 1: Identify the first term and common difference
The first term \( a \) of the sequence is:
\[ a = 0.6 \]

Next, we need to find the common difference \( d \). We can calculate it by subtracting the first term from the second term:
\[ d = 1.7 - 0.6 = 1.1 \]

### Step 2: Use the formula for the nth term of an AP
The formula for the nth term \( T_n \) of an arithmetic progression is given by:
\[ T_n = a + (n - 1) \cdot d \]

### Step 3: Substitute the values into the formula
We need to find the 14th term, so we will set \( n = 14 \):
\[ T_{14} = 0.6 + (14 - 1) \cdot 1.1 \]

### Step 4: Calculate \( T_{14} \)
Now, simplify the expression:
\[ T_{14} = 0.6 + 13 \cdot 1.1 \]

Calculating \( 13 \cdot 1.1 \):
\[ 13 \cdot 1.1 = 14.3 \]

Now, add this to the first term:
\[ T_{14} = 0.6 + 14.3 = 14.9 \]

### Final Answer
The 14th term of the arithmetic progression is:
\[ T_{14} = 14.9 \]

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