Pattern 1 → 6 circles = 1 × 5 + 1
Pattern 2 → 13 circles = 2 × 6 + 1
Pattern 3 → 22 circles = 3 × 7 + 1
Pattern 4 → 33 circles = 4 × 8 + 1

Notice that the number of circles for a particular pattern is always equal to :

(Pattern number) × (Pattern number + 4) + 1

For pattern 97, we have 97 × 101 + 1
For pattern 98, we have 98 × 102 + 1

Difference between the two patterns
= 98 × 102 - 97 × 101
= 98 × 1 + 98 × 101 - 97 × 101
= 98 + 101
= 98 + 98 + 3
= 199

So we can also generalise that the difference between any 2 consecutive patterns is always equal to :

(Bigger pattern number × 2) + 3


Alternatively,

Difference between the two patterns
= 98 × 102 - 97 × 101
= 1 × 102 + 97 × 102 - 97 × 101
= 102 + 97
= 5 + 97 + 97
= 199

So we can also generalise that the difference between any 2 consecutive patterns is always equal to :

(Smaller pattern number × 2) + 5