Find an equation for the nth term of the sequence. -4, -16, -64, -256, …

Solution:

The geometric series formula refers to the formula that gives the sum of a finite geometric sequence, the sum of an infinite geometric series, and the nth term of a geometric sequence.

The given sequence is -4, -16, -64, -256, …

Here

a₁ = -4

r = -16/-4 = 4

The formula to find the nth term of the geometric sequence is

a_n = a₁.r^{(n - 1)}

Substituting the values

a_n = -4.4^{(n - 1)}

Therefore, the nth term of the sequence is a_n = -4.4^{(n - 1)}.

Find an equation for the nth term of the sequence. -4, -16, -64, -256, …

Summary:

The equation for the nth term of the sequence -4, -16, -64, -256, … is a_n = -4.4^{(n - 1)}.