Which term in the A.P. ` 68,64,60` is -`8`?

Answer

To find which term in the arithmetic progression (A.P.) 68, 64, 60, ... is -8, we can follow these steps:

### Step 1: Identify the first term (a) and the common difference (d)
- The first term \( a = 68 \).
- The common difference \( d \) can be calculated as:
\[ d = 64 - 68 = -4 \]

### Step 2: Write the formula for the nth term of an A.P.
The formula for the nth term \( a_n \) of an A.P. is given by:
\[ a_n = a + (n - 1) \cdot d \]

### Step 3: Set the nth term equal to -8
We want to find \( n \) such that:
\[ a_n = -8 \]
Substituting the values of \( a \) and \( d \) into the formula:
\[ -8 = 68 + (n - 1)(-4) \]

### Step 4: Simplify the equation
Rearranging the equation:
\[ -8 = 68 - 4(n - 1) \]
Distributing the -4:
\[ -8 = 68 - 4n + 4 \]
Combining like terms:
\[ -8 = 72 - 4n \]

### Step 5: Solve for n
Now, isolate \( n \):
\[ -8 - 72 = -4n \]
\[ -80 = -4n \]
Dividing both sides by -4:
\[ n = \frac{-80}{-4} = 20 \]

### Conclusion
Thus, -8 is the **20th term** of the arithmetic progression.

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