Which term of the a.P. : `24,20,16, ....` is zero?

Answer

To find which term of the arithmetic progression (A.P.) \(24, 20, 16, \ldots\) is zero, we can follow these steps:

### Step 1: Identify the first term (a) and the common difference (d)
The first term \(a\) of the A.P. is \(24\).
To find the common difference \(d\), we subtract the second term from the first term:
\[ d = 20 - 24 = -4 \]

### Step 2: Write the formula for the n-th term of the A.P.
The formula for the n-th term \(a_n\) of an A.P. is given by:
\[ a_n = a + (n - 1)d \]
Substituting the values of \(a\) and \(d\):
\[ a_n = 24 + (n - 1)(-4) \]

### Step 3: Set the n-th term equal to zero
We want to find the term that is zero, so we set \(a_n\) to zero:
\[ 0 = 24 + (n - 1)(-4) \]

### Step 4: Solve for n
Rearranging the equation:
\[ 0 = 24 - 4(n - 1) \]
\[ 4(n - 1) = 24 \]
Dividing both sides by 4:
\[ n - 1 = 6 \]
Adding 1 to both sides:
\[ n = 7 \]

### Conclusion
The 7th term of the A.P. is zero.

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