Write the 5th and 8th terms of an AP whose 10th term is 43 and the common difference is 4.

Answer

To find the 5th and 8th terms of an arithmetic progression (AP) where the 10th term is 43 and the common difference is 4, we can follow these steps:

### Step 1: Understand the formula for the nth term of an AP
The nth term of an AP can be expressed as:
\[ a_n = a + (n - 1) \cdot d \]
where:
- \( a_n \) is the nth term,
- \( a \) is the first term,
- \( d \) is the common difference,
- \( n \) is the term number.

### Step 2: Use the information given for the 10th term
We know that the 10th term \( a_{10} \) is 43 and the common difference \( d \) is 4. Thus, we can write:
\[ a_{10} = a + (10 - 1) \cdot d \]
Substituting the known values:
\[ 43 = a + 9 \cdot 4 \]

### Step 3: Solve for \( a \)
Now, simplify the equation:
\[ 43 = a + 36 \]
To find \( a \), subtract 36 from both sides:
\[ a = 43 - 36 \]
\[ a = 7 \]

### Step 4: Calculate the 5th term
Now that we have \( a \) and \( d \), we can find the 5th term \( a_5 \):
\[ a_5 = a + (5 - 1) \cdot d \]
Substituting the values:
\[ a_5 = 7 + 4 \cdot 4 \]
\[ a_5 = 7 + 16 \]
\[ a_5 = 23 \]

### Step 5: Calculate the 8th term
Next, we calculate the 8th term \( a_8 \):
\[ a_8 = a + (8 - 1) \cdot d \]
Substituting the values:
\[ a_8 = 7 + 7 \cdot 4 \]
\[ a_8 = 7 + 28 \]
\[ a_8 = 35 \]

### Final Answer
The 5th term of the AP is 23, and the 8th term is 35.

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