The first few terms of a geometric sequence are given by 1, 2, 4, 8… What is the value of the 20th term divided by the 18th term?

Answer 1

a₂₀/a₁₈ = r² = 2² = 4

Answer 2

1,2,4,8,...

a1 = 1

a2 = 2

a3 = 4

a4 = 8

...

an =a1(r)^(n-11) = (r)^(n-1)

r = 2

an+ (2)^(n-1)

a20 = r^19

a18 = r^17

a20/a18 = r^19/r^17 = r^2 = (2)^2 = 4

a(n+2)/an = 4

a3/a1 = 4/1 = 4

a5/a2 = 8/2 = 4

a6/a3 = 16/4 = 4

any term divided by 2 terms before = 4