Question

What is the seventh term of the geometric sequence were a one equals -4096 and a four equals 64

Answer 1

-1

Explanation:

The nth term of a geometric sequence is:

aₙ = a₁ (r)ⁿ⁻¹

where a₁ is the first term and r is the common ratio.

Given that a₁ = -4096 and a₄ = 64:

64 = -4096 (r)⁴⁻¹

-1/64 = r³

r = -1/4

So the seventh term is:

a₇ = -4096 (-1/4)⁷⁻¹

a₇ = -1