Find the 100th term of the sequence:
`sqrt3, 2sqrt3, 3sqrt3`,…..

Answer

To find the 100th term of the sequence given by \( \sqrt{3}, 2\sqrt{3}, 3\sqrt{3}, \ldots \), we can follow these steps:

### Step 1: Identify the first term and the common difference
The first term \( a \) of the sequence is:
\[ a = \sqrt{3} \]

To find the common difference \( d \), we subtract the first term from the second term:
\[ d = a_2 - a_1 = 2\sqrt{3} - \sqrt{3} = \sqrt{3} \]

### Step 2: Use the formula for the nth term of an arithmetic progression
The formula for the nth term \( a_n \) of an arithmetic progression is given by:
\[ a_n = a + (n - 1) \cdot d \]
Here, we need to find the 100th term, so we set \( n = 100 \).

### Step 3: Substitute the values into the formula
Substituting \( a \), \( d \), and \( n \) into the formula:
\[ a_{100} = a + (100 - 1) \cdot d \]
\[ a_{100} = \sqrt{3} + (99) \cdot \sqrt{3} \]

### Step 4: Simplify the expression
Now, we can simplify the expression:
\[ a_{100} = \sqrt{3} + 99\sqrt{3} = 100\sqrt{3} \]

### Conclusion
Thus, the 100th term of the sequence is:
\[ \boxed{100\sqrt{3}} \]