What is the 7th term of the geometric sequence where a₁ = -4,096 and a₄ = 64?

Solution:

Solution:

The nth term of the geometric sequence is given by,:

a_n = a · r^{n - 1}.

Here a and r being the first term and the common ratio respectively.

Given:

a₁ = a = -4096 and a₄ = 64

a₄ = a. r^{4 - 1}

64 = -4096 × r³

r³ = 64/(-4096) = -1/64

r = - 1/4

Substituting the value of a and r in the formula for a7, we get

a₇ = a. r^{7 - 1} = a . r⁶

a₇ = -4096× (-1/4)⁶

a₇ = -4096/4096

a₇ = -1

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What is the 7th term of the geometric sequence where a₁ = -4,096 and a₄ = 64?

Summary:

The 7th term of the geometric sequence where a₁ = -4,096 and a₄ = 64 is -1.