Which term of the A.P. 4.2, 4.7,5.2,5.7….. Is 8.7?

Answer

To find which term of the arithmetic progression (A.P.) 4.2, 4.7, 5.2, 5.7, ... is equal to 8.7, 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:
\[ a = 4.2 \]
To find the common difference \( d \), we subtract the first term from the second term:
\[ d = a_2 - a_1 = 4.7 - 4.2 = 0.5 \]

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

### Step 3: Set the nth term equal to 8.7 and substitute the values of a and d
We need to find \( n \) such that:
\[ T_n = 8.7 \]
Substituting the values of \( a \) and \( d \):
\[ 8.7 = 4.2 + (n - 1) \cdot 0.5 \]

### Step 4: Solve for \( n \)
First, isolate the term involving \( n \):
\[ 8.7 - 4.2 = (n - 1) \cdot 0.5 \]
Calculating the left side:
\[ 4.5 = (n - 1) \cdot 0.5 \]
Next, divide both sides by 0.5:
\[ n - 1 = \frac{4.5}{0.5} \]
Calculating the right side:
\[ n - 1 = 9 \]
Now, add 1 to both sides:
\[ n = 10 \]

### Conclusion
The term 8.7 is the 10th term of the A.P.

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