The 15th term of the A.P. 7,13, 19, …………… is:

Options

A. 105
B. `-78`
C. `97`
D. `91`

Answer

To find the 15th term of the arithmetic progression (A.P.) given as 7, 13, 19, ..., we can follow these steps:

### Step 1: Identify the first term and the common difference
The first term \( a \) of the A.P. is the first number in the sequence:
\[ a = 7 \]

Next, we need to find the common difference \( d \). The common difference is calculated by subtracting the first term from the second term:
\[ d = 13 - 7 = 6 \]

### 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:
\[ T_n = a + (n-1) \cdot d \]

### Step 3: Substitute the values into the formula
We want to find the 15th term, so we set \( n = 15 \):
\[ T_{15} = a + (15-1) \cdot d \]
\[ T_{15} = 7 + (14) \cdot 6 \]

### Step 4: Calculate the value
Now, we calculate:
\[ T_{15} = 7 + 84 \]
\[ T_{15} = 91 \]

### Final Answer
The 15th term of the A.P. is:
\[ \boxed{91} \]

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