Question

Write a rule for the nth term of the geometric sequence for which a1=−6 and a5=−486

Answer 1

The geometric rule for the nth term of the geometric sequence for which a1 =−6 and a5=−486 is -6 × 3^(n - 1)

The nth term of a geometric sequence

First term, a1 = -6

Fifth term, a5 = -486

a5 = ar^(n - 1)

-486 = -6 × r^(5-1)

-486 = -6r⁴

r⁴ = -486 / 6

r⁴ = 81

r = 4√81

r = 3

Geometric rule:

nth term = ar^(n-1)

nth term = -6 × 3^(n - 1)

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