For the geometric sequence with a1 = 3 and r = 1/2, what is a6?

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Multiple Choice

For the geometric sequence with a1 = 3 and r = 1/2, what is a6?

Explanation:
In a geometric sequence, each term is obtained by multiplying the previous term by the common ratio, so a_n = a_1 r^{n-1}. With a1 = 3 and r = 1/2, the sixth term is a6 = 3 * (1/2)^{5} = 3/32. This reflects applying the ratio five times after the first term. The other values would correspond to different numbers of halvings: 3/16 is after four halvings (a5), 3/64 is after six halvings (a7), and 9/32 would not fit this sequence with the given a1 and r.

In a geometric sequence, each term is obtained by multiplying the previous term by the common ratio, so a_n = a_1 r^{n-1}. With a1 = 3 and r = 1/2, the sixth term is a6 = 3 * (1/2)^{5} = 3/32. This reflects applying the ratio five times after the first term. The other values would correspond to different numbers of halvings: 3/16 is after four halvings (a5), 3/64 is after six halvings (a7), and 9/32 would not fit this sequence with the given a1 and r.

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