ACT Math · Sequences and series

A sequence is defined by a_n = 3n - 2. What is a_10?

A sequence is defined by an=3n−2a_n = 3n - 2. What is a10a_{10}?

Answer and explanation

Answer: J: 28

Substitute n=10n=10 into the rule: a10=3(10)−2=30−2=28a_{10}=3(10)-2=30-2=28, choice J. Choice H (3030) drops the −2-2 and gives only 3n3n. Choice G (3232) adds 22 instead of subtracting it, since 30+2=3230+2=32. Choice F (1818) corresponds to n=203n=\frac{20}{3}, not a term number, so it does not follow from the formula for any valid nn. As a check, the sequence 1,4,7,10,…1, 4, 7, 10,\dots increases by 33 each term, so by the tenth term it has grown by 9⋅3=279\cdot3=27 from the first term, giving 1+27=281+27=28, which agrees with the substitution.

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