Algebra-1

Given that a₅ = 486 and a₈ = 13122, 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:

a₅ = a₁ * r^(5-1)

a₈ = a₁ * r^(8-1)

 

Substituting the given values, we have:

486 = a₁ * r⁴

13122 = a₁ * r⁷

 

We can solve the first equation for a₁:

a₁ = 486 / r⁴

 

Substituting this expression for a₁ into the second equation:

13122 = (486 / r⁴) * r⁷...