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A

Anonymous

Oct 12, 2024

What is the 6th term of the geometric sequence where a1 = -4,096 and a4 = 64?A. -1B. 4C. 1D. -4?

What is the 6th term of the geometric sequence where the first term ( a_1 = -4,096 ) and the fourth term ( a_4 = 64 )? A. -1 B. 4 C. 1 D. -4

2 Answers

A
Anonymous

Feb 18, 2025

Let r be the common ratio of the geometric sequence.

a₁ = -4096

a₄ = 64

-4096 × r³ = 64

r³ = -64/4096

r³ = -1/64

r = -1/4

a₆ = a₁ r⁵

a₆ = -4096 × (-1/4)⁵

a₆ = 4

…… The answer: B. 4

A
Anonymous

Dec 28, 2024

a_4 = a_1 * r^(4 – 1)

64 = -4096r^3

-1/64 = r^3

r = -1/4

a_6 = a_4 * (-1/4)^(6 – 4)

a_6 = 64 * 1/16 = 4

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