Each problem is a sequence with one term missing: 30, 25, ___, 15, 10, 5. Some count on, some count back, and some double or triple. Finding the gap means working out the rule first.
The blank is rarely at the end, and that is the point. A sequence ending in a blank can be finished by adding to the last number without ever noticing what the pattern is; a gap in the middle cannot. Terms Shown sets how much of the sequence is given - more terms make the rule easier to spot but put the gap further from an edge.
A sequence built by the same rule each step: add 5, subtract 5, double. Once you know the rule you can fill any gap in it, forwards or backwards.
Compare two terms that are next to each other to find the step, then check it holds across the whole sequence before applying it to the gap. Two terms are enough to guess with and three are enough to be sure.
Because a blank at the end can be filled without understanding the pattern - you add the step to the last number and stop. A gap in the middle has to be reached from both sides.
Third and fourth grade for counting on and back, and fourth and fifth for doubling and tripling patterns.