ACT Math · Sequences and series

A geometric sequence has first term 3 and common ratio 2. What is the 6th term?

A geometric sequence has first term 3 and common ratio 2. What is the 6th term?

Answer and explanation

Answer: C: 96

In a geometric sequence an=a1rn−1a_n=a_1r^{n-1}. With a1=3a_1=3 and r=2r=2, the sixth term is a6=3⋅25=3⋅32=96a_6=3\cdot2^5=3\cdot32=96, choice C. Listing terms confirms it: 3,6,12,24,48,963, 6, 12, 24, 48, 96. Choice D (192192) uses an exponent of 66 instead of 55, which is the seventh term. Choice B (3636) is 3⋅123\cdot12 or 6⋅66\cdot6, which does not follow the pattern. Choice A (1818) is 3⋅63\cdot6, treating the sequence as arithmetic-style multiplication by the term number. Remember that the exponent is one less than the term number.

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