The 4th term from the end of an AP -11, -8, -5, …, 49 is

Options

A. 37
B. 40
C. 43
D. 58

Answer

To find the 4th term from the end of the arithmetic progression (AP) given as -11, -8, -5, ..., 49, we can follow these steps:

### Step 1: Identify the AP and its properties
The given AP is: -11, -8, -5, ..., 49.

### Step 2: Reverse the AP
To find the 4th term from the end, we can reverse the sequence. The reversed AP will be: 49, ..., -5, -8, -11.

### Step 3: Determine the first term and common difference
In the reversed AP:
- The first term (a) is 49.
- To find the common difference (d), we can subtract the second term from the first term. The second term in the reversed AP is -5.

\[ d = -5 - 49 = -54 \]

However, we should calculate the common difference correctly:
The common difference can also be calculated as:
\[ d = -8 - (-11) = -8 + 11 = 3 \]

### Step 4: Calculate the 4th term from the start
Since the 4th term from the end is the same as the 4th term from the start in the reversed AP, we need to find \( a_4 \).

The formula for the nth term of an AP is given by:
\[ a_n = a + (n - 1) \cdot d \]
For \( n = 4 \):
\[ a_4 = a + (4 - 1) \cdot d = 49 + 3 \cdot 3 \]

### Step 5: Substitute the values
Now, substituting the values:
\[ a_4 = 49 + 9 = 58 \]

### Step 6: Conclusion
Thus, the 4th term from the end of the AP is 58.