If the eighth term of a geometric sequence is -49152, and the eleventh term of an geometric sequence is -3145728 what is the first term and the common ratio?

Question

If the eighth term of a geometric sequence is -49152, and the eleventh term of an geometric sequence is -3145728
its first term
a1=

and common ratio r = 

Answer 1

a₁r⁷ = -49152

 

a₁r¹⁰ = -3145728  

 

a₁ = -49152/r⁷

 

(-49152/r⁷)(r¹⁰) = -3145728

 

-49152r³ = -3145728

 

r³ = 3145728/-49152 = 64

 

r = ³√64

 

r = 4

 

a₁ = -49152/r⁷

 

a₁ = -49152/4⁷

 

a₁ = -3