• You’ve appended all numbers into StringBuilder but printed the result only once after the loop, which outputs the entire sequence in one single line, not step-by-step as you want.
• Also, the numbers were appended directly without any space, resulting in a single concatenated string like 12345

Here is the corrected version:

import java.util.Scanner;

public class Series {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        System.out.print("Insert number: ");
        int a = sc.nextInt();
        sc.close();

        StringBuilder sb = new StringBuilder();
        for (int i = 1; i <= a; i++) {
            sb.append(i).append(" ");
            System.out.println(sb.toString().strip());
        }
    }
}

Result

Insert number: 10
1
1 2
1 2 3
1 2 3 4
1 2 3 4 5
1 2 3 4 5 6
1 2 3 4 5 6 7
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9 10

• We should have added an if condition and avoided using strip() (or trim()) here for efficiency:

import java.util.Scanner;

public class Series {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        System.out.print("Insert number: ");
        int a = sc.nextInt();
        sc.close();

        StringBuilder sb = new StringBuilder();
        for (int i = 1; i <= a; i++) {
            if (i > 1) {
                sb.append(" ");
            }

            sb.append(i);
            System.out.println(sb.toString());
        }
    }
}

• Without using StringBuilder():

import java.util.Scanner;

public class Series {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        System.out.print("Insert number: ");
        int a = sc.nextInt();
        sc.close();

        if (a < 1) {
            System.out.println("");
            return;
        }

        String res = "1";
        System.out.println(res);
        for (int i = 2; i <= a; i++) {
            res += " " + i;
            System.out.println(res);
        }
    }
}

• Using two-loops approach is more memory-efficient as it avoids using StringBuilder(). The numbers are printed directly as they are processed, with no intermediate storage required.

import java.util.Scanner;

public class Series {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        System.out.print("Insert number: ");
        int a = sc.nextInt();
        sc.close();

        for (int i = 1; i <= a; i++) {
            for (int j = 1; j <= i; j++) {
                System.out.print(j + " ");
            }
            System.out.println();
        }
    }
}

Notes

I would recommend making a habit of calling one of the String#strip…
methods rather than trim. See the post: Java’s String.trim has a
strange idea of whitespace. And see more discussion on this Answer of
mine. – Comment from Basil Bourque

The trim() or if can be avoided by starting with “1” in the
StringBuilder and looping from 2 on. (actually I would suggest using
a plain String instead of a SringBuilder) – by
user85421

You could also do it like this sans StringBuilder. And I don’t see the need to trim the white space unless it is a requirement.

Scanner scanner = new Scanner(System.in);
System.out.print("Insert number ");
int max = scanner.nextInt();

String s = "";
for (int i = 1; i <= max; i++) {
    s += i + " ";
    System.out.println(s);
}

If you must trim the trailing white space you could do the following since there is only one space to remove.

  System.out.println(s.substring(0, s.length()-1));