ACT-Style: Sequence Pattern Recognition

ACT Math · Axiom Academy

EXAMPLE ACT-Style: Sequence Pattern Recognition Spotting a geometric pattern and finding a term far down the list In the sequence , each term after the first is found by multiplying the previous term by a constant. What is the 7th term of the sequence? Every "find the Nth term" ACT question starts with the same fork: is the pattern arithmetic (constant difference) or geometric (constant ratio)? Check the ratio between consecutive terms first: , , — a constant ratio means GEOMETRIC, not arithmetic. Geometric formula: a_n = a_1 r^ n-1 , where a_1 is the first term, r is the common ratio, and n is the term number you want. Watch the exponent: it's n-1 , not n — the 7th term uses r^6 , not r^7 . That off-by-one is the single most common slip on this question type. Don't reach for the arithmetic formula out of habit — confirm constant DIFFERENCE vs constant RATIO before picking a formula, every time.

This is the written version of the interactive lesson above. See the full ACT Math course.