Find the 24th term of the sequence: 12,10,8,6…..

Answer

To find the 24th term of the sequence 12, 10, 8, 6, we can follow these steps:

### Step 1: Identify the first term (a) and the common difference (d)
- The first term \( a \) of the sequence is 12.
- To find the common difference \( d \), we subtract the first term from the second term:
\[ d = a_2 - a_1 = 10 - 12 = -2 \]

### Step 2: Use the formula for the nth term of an arithmetic progression
- The formula for the nth term \( a_n \) of an arithmetic progression is given by:
\[ a_n = a + (n - 1) \cdot d \]
- Here, we need to find the 24th term, so we set \( n = 24 \).

### Step 3: Substitute the values into the formula
- Substitute \( a = 12 \), \( n = 24 \), and \( d = -2 \) into the formula:
\[ a_{24} = 12 + (24 - 1) \cdot (-2) \]
- This simplifies to:
\[ a_{24} = 12 + 23 \cdot (-2) \]

### Step 4: Calculate the value
- Now calculate \( 23 \cdot (-2) \):
\[ 23 \cdot (-2) = -46 \]
- Substitute this back into the equation:
\[ a_{24} = 12 - 46 \]
- Finally, calculate:
\[ a_{24} = -34 \]

### Final Answer
The 24th term of the sequence is \( -34 \).

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