What is the 10th term of the sequence 64, 16, 4

Solution:

The sequence 64, 16, 4 ….is a geometric series with

Common ratio = r = 16/64 = 4/16 = 1/4

The first term is a = 64

The nth term of a geometric series is given as

T_n = ar^{n - 1}

T₁₀ = 64(1/4)^{10 - 1}

= 64(1/4)⁹

= 4³ × 4^-9

= 4^-6

= 1/4⁶

= 1/4096

What is the 10th term of the sequence 64, 16, 4

Summary:

The 10th term of the sequence 64, 16, 4 is 1/4⁶ or 1/4096