Find the sum of the 4th term and 9th term of the A.P..
3,8,13,18,.... .

Answer

To find the sum of the 4th term and the 9th term of the given arithmetic progression (A.P.) 3, 8, 13, 18, ..., we can follow these steps:

### Step 1: Identify the first term and the common difference
The first term (A) of the A.P. is the first number in the sequence, which is:
\[ A = 3 \]

To find the common difference (D), we subtract the first term from the second term:
\[ D = A_2 - A_1 = 8 - 3 = 5 \]

### Step 2: Find the 4th term (A4)
The formula for the nth term of an A.P. is given by:
\[ A_n = A + (n - 1) \cdot D \]

For the 4th term (n = 4):
\[ A_4 = A + (4 - 1) \cdot D \]
\[ A_4 = 3 + (3) \cdot 5 \]
\[ A_4 = 3 + 15 \]
\[ A_4 = 18 \]

### Step 3: Find the 9th term (A9)
Using the same formula for the 9th term (n = 9):
\[ A_9 = A + (9 - 1) \cdot D \]
\[ A_9 = 3 + (8) \cdot 5 \]
\[ A_9 = 3 + 40 \]
\[ A_9 = 43 \]

### Step 4: Calculate the sum of the 4th and 9th terms
Now, we can find the sum of the 4th term and the 9th term:
\[ A_4 + A_9 = 18 + 43 \]
\[ A_4 + A_9 = 61 \]

### Final Answer
The sum of the 4th term and the 9th term of the A.P. is:
\[ \text{Sum} = 61 \]

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