In a geometric sequence with a1 = 4 and r = -3, what is a6?

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Multiple Choice

In a geometric sequence with a1 = 4 and r = -3, what is a6?

Explanation:
Geometric sequences multiply by a constant ratio each step, so the nth term is a1 times r^(n-1). With a1 = 4 and r = -3, the sixth term is a6 = 4 * (-3)^(6-1) = 4 * (-3)^5. Since (-3)^5 equals -243, a6 = 4 * (-243) = -972. The negative sign comes from multiplying by -3 an odd number of times, and the magnitude grows as 3^5 (243) times the starting value.

Geometric sequences multiply by a constant ratio each step, so the nth term is a1 times r^(n-1). With a1 = 4 and r = -3, the sixth term is a6 = 4 * (-3)^(6-1) = 4 * (-3)^5. Since (-3)^5 equals -243, a6 = 4 * (-243) = -972. The negative sign comes from multiplying by -3 an odd number of times, and the magnitude grows as 3^5 (243) times the starting value.

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