Algebra-1

Given that a₆ = -96 and a₉ = 768, we can use these two terms to determine the common ratio (r) and subsequently find the first term (a₁).

 

Using the formula for the nth term of a geometric sequence, we can write two equations:

a₆ = a₁ * r^(6-1)

a₉ = a₁ * r^(9-1)

 

Substituting the given values, we have:

-96 = a₁ * r⁵

768 = a₁ * r⁸

 

We can solve the first equation for a₁:

a₁ = -96 / r⁵

Substituting this expression for a1 into the second equation:

768 = (-96 / r⁵) * r⁸