Algebra-1

Given that a₈ = 1152 and a₁₃ = 36864, 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:

a₈ = a₁ * r(^8-1)

a₁₃ = a₁ * r^(13-1)

Substituting the given values, we have:

1152 = a₁ * r⁷

36864 = a₁ * r¹²

We can solve the first equation for a₁:

a₁ = 1152 / r⁷

Substituting this expression for a₁ into the second equation:

36864 = (1152 / r⁷) * r¹²