Find the `10^(th)` term of the sequence 10, 8, 6, .........

Answer

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

### Step 1: Identify the first term and common difference
The first term \( a \) of the sequence is 10. To find the common difference \( d \), we subtract the second term from the first term:
\[ d = a_2 - a_1 = 8 - 10 = -2 \]

### Step 2: Verify the common difference
To ensure that the sequence is an arithmetic progression (AP), we can check the difference between the third term and the second term:
\[ d = a_3 - a_2 = 6 - 8 = -2 \]
Since the common difference is consistent, we confirm that this is an AP.

### Step 3: Use the formula for the nth term of an AP
The formula for the nth term \( a_n \) of an arithmetic progression is given by:
\[ a_n = a + (n - 1) \cdot d \]
where \( a \) is the first term, \( n \) is the term number, and \( d \) is the common difference.

### Step 4: Substitute values to find the 10th term
We need to find the 10th term, so we set \( n = 10 \):
\[ a_{10} = 10 + (10 - 1) \cdot (-2) \]
Calculating this gives:
\[ a_{10} = 10 + 9 \cdot (-2) \]
\[ a_{10} = 10 - 18 \]
\[ a_{10} = -8 \]

### Final Answer
The 10th term of the sequence is \(-8\).

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