I need a solution for this pattern in easy way.

The pattern is a repeating sequence of '*' and '+' split into lines, where the length of each line is equal to the line number, starting from line 1.The modulus operator is excellent for for iterating over a sequence. So keep a count of the characters printed, use count % 2 to alternate between the two characters then print a carrage return when the number of characters in the line is equal to the line number.

static void Main(string[] args)
       {
           int count = 0;
           for (int line = 1; line <= 5; line++)
           {
               int lineEnd = count + line;
               while (count < lineEnd)
               {
                   Console.Write(count % 2 == 0 ? '*' : '+');
                   count++;
               }
               Console.WriteLine();
           }
           Console.ReadKey();
       }

A more flexible but less simple approach is to use a method that can handle any repeating pattern of any length.

static void PrintPattern(string pattern,int lines)
     {
         //To do:check for valid arguments
         int count = 0;
         for (int line = 1; line <= lines; line++)
         {
             int lineEnd = count + line;
             while (count < lineEnd)
             {
                 Console.Write(pattern[count % pattern.Length]);
                 count++;
             }
             Console.WriteLine();
         }
         Console.ReadKey();
     }

Quote:

I need a solution for this pattern in easy way.

The only easy way is having someone paid to do the job.
As programmer, your job is to create algorithms
First of all, analyze the problem:
1) the shape is a triangle
2) each line is made of alternated + and *
3) lines 1, 4 and 5 start with *, lines 2 and 3 start with +

You forgot to state a problem with your code

static void Main(string[] args)
{
    int n = Convert.ToInt32(Console.ReadLine());
    int offset;
    for(int i = 0; i <= n; i++)
    {
        offset = 0;
        for (int j = 0; j <= i; j++)
        {
            if ((j + offset) % 2)
            {
                Console.Write("*");
            }
            else
            {
                Console.Write("+");
            }
        }
        Console.WriteLine();
    }
    Console.ReadKey();
}

This code will print a triangle (1) with alternating * and + (2).
you just have to find how to change offset = 0 to follow starting char pattern (3).