ACT Preparation / Unit 15 ACT 1433 worked example, 60 to 90 seconds
Finding a Term of a Sequence
The idea
A sequence term is found in three steps. First, decide whether the sequence adds or multiplies: check the differences, then the ratios. Second, find a₁ and the common difference or ratio. Third, substitute n into the matching formula, counting n − 1 steps from the first term.
In practice
Worked example: 7, 11, 15, 19 has a common difference of 4, so the 50th term is 7 + 49 × 4 = 203. Second: 2, 6, 18, 54 has a common ratio of 3, so the 8th term is 2 × 3⁷ = 4,374. Third: if an arithmetic sequence has a₃ = 10 and a₇ = 26, four steps add 16, so d = 4 and a₁ = 2.
Where people slip
Counting steps is where answers slip: from the 3rd term to the 7th is 4 steps, not 5.
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