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

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

• A. 3/32
• B. 3/16
• C. 3/64
• D. 9/32

Answer: (A)

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.