Complete the number pattern:

Question

486, 162, 54, 18

Answer 1

a1 = 486

a2 =162

a3 =54

a4 =18

a2 / a1 = 162 / 486 = 1 / 3

a3 / a2 = 54 / 162 = 1 / 3

a4 / a3 = 18 / 54 = 1 / 3

That is Geometric progression with first term a1 = 486 and a common ratio of r = 1 / 3.

In GP n-th term is:

an = a1 ∙ rⁿ ⁻ ¹

In this case:

an = 486 ∙ ( 1 / 3 )ⁿ ⁻ ¹

By the way in GP:

an = a(n-1) ∙ r

Next two terms are:

a5 = a4 ∙ 1 / 3 = 18 ∙ 1 / 3 = 6

and

a6 = a5 ∙ 1 / 3 = 6 ∙ 1 / 3 = 2