The `n^(th)` term of the AP in 2,5,8 …. Is

Options

A. `3n-1`
B. `2n-1`
C. `3n-2`
D. `2n-3`

Answer

To find the nth term of the arithmetic progression (AP) given as 2, 5, 8, ..., we can follow these steps:

### Step 1: Identify the first term (a) and the common difference (d)
- The first term \( a \) of the AP is 2.
- The common difference \( d \) can be found by subtracting the first term from the second term:
\[ d = 5 - 2 = 3 \]

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

### Step 3: Substitute the values of \( a \) and \( d \) into the formula
- Now, substituting \( a = 2 \) and \( d = 3 \) into the formula:
\[ a_n = 2 + (n - 1) \cdot 3 \]

### Step 4: Simplify the expression
- Distributing the 3:
\[ a_n = 2 + 3n - 3 \]
- Combining like terms:
\[ a_n = 3n - 1 \]

### Conclusion
- Therefore, the nth term of the AP is:
\[ a_n = 3n - 1 \]