Asked by Scarlet
Complete the number pattern:
486, 162, 54, 18
486, 162, 54, 18
Answers
Answered by
Bosnian
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
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
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