Find the 15th term of the arithmetic progression 10, 4, -2, ….

Options

A. `-721=`
B. `-74`
C. `-76`
D. `-78`

Explanation

To find the 15th term of the arithmetic progression (AP) given by the series 10, 4, -2, ..., we can follow these steps:

### Step 1: Identify the first term (a) and the common difference (d)
The first term \( a \) is the first number in the series:
\[ a = 10 \]

To find the common difference \( d \), we subtract the first term from the second term:
\[ d = 4 - 10 = -6 \]

### 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 to find the 15th term
We need to find the 15th term, so we set \( n = 15 \):
\[ T_{15} = a + (15 - 1) \cdot d \]

Substituting the values of \( a \) and \( d \):
\[ T_{15} = 10 + (15 - 1) \cdot (-6) \]
\[ T_{15} = 10 + 14 \cdot (-6) \]

### Step 4: Calculate the value
Now, calculate \( 14 \cdot (-6) \):
\[ 14 \cdot (-6) = -84 \]

Now substitute this back into the equation:
\[ T_{15} = 10 - 84 \]
\[ T_{15} = 10 - 84 = -74 \]

### Final Answer
The 15th term of the arithmetic progression is:
\[ T_{15} = -74 \]

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