Inductive Reasoning
Number series
Classify the series before computing. Check arithmetic (constant addition), geometric (constant multiplier), second-order differences (the differences themselves follow a pattern), interleaved alternating series, squares or cubes plus an offset, and primes. If the differences run 4, 6, 8, 10, the rule is not "add 4" but "add successive even numbers."
Letter series
Convert letters to positions with A = 1 through Z = 26. Remember EJOTY (E = 5, J = 10, O = 15, T = 20, Y = 25) so you can jump without counting on your fingers. Watch for wrap-around past Z and for reverse-alphabet sequences.
Figural series
Track one feature at a time: rotation direction and amount, reflection, number of sides or strokes, shading, dot position, and additive or subtractive elements. A figure rotating 90° clockwise each step is not equivalent to one reflecting across a vertical axis, and answer options usually include both.
Odd-one-out and matrices
Find the attribute shared by all but one item. In 3×3 matrices, read rows before columns, and test whether the third cell is a sum, a rotation, or a subtraction of the first two.
Trap
Several rules can fit three terms. Verify a candidate rule against every given term before committing.
Worked example
2, 6, 12, 20, 30, ? - differences are 4, 6, 8, 10, so the next difference is 12 and the answer is 42. The underlying rule is n(n+1).