Determine the common ratio and find the next three terms of the geometric sequence t8, t5, t2

The common ratio of the given geometric sequence is the number that is multiplied to the first term in order to get the second term. Consequently, this is also the number multiplied to the second term to get the third term. This cycle goes on and on until a certain term is acquired. In this item, the common ratio r is,

r = t⁵/t⁸ = t²/t⁵

The answer, r = t⁻³.

The next three terms are,

n₄ = (t²) (t⁻³) = t⁻¹

n₅ = (t⁻¹) (t⁻³) = t⁻⁴

n₆ = (t⁻⁴) (t⁻³) = t⁻⁷

The answers for the next three terms are as reflected above as n₄, n₅, and n₆, respectively.

T^5/t^8=t^ (5-8) = t^ (-3)

t^2/t^5=t^ (2-5) = t^ (-3)

The common ratio is t^ (-3)

The next three terms are:

t^2*t^ (-3) = t^ (2-3) = t^ (-1)

t^ (-1) * t^ (-3) = t^ (-1-3) = t^ (-4)

t^ (-4) * t^ (-3) = t^ (-4-3) = t^ (-7)

Answer: The next three terms of the geometric sequence t^8, t^5, t^2 are:

t^ (-1), t^ (-4), t^ (-7)