Geometric sequence help?

Question

For a given geometric sequence, the 6th term, a6 is equal to 37/4, and the 9th term, a9, is equal to -74. Find the value of the
13th term, a13. If applicable, write your answer as a fraction.

Answer 1

Let r be the common ratio of the sequence

 

a₆ = 37/4      a₇ = (37/4)r      a₈ = (37/4)r²      a₉ = (37/4)r³ = -74

 

                                                                                      r³ = -74(4/37) = -8

 

                                                                                     So, r = -2

 

a₆ = a₁r⁵    So, 37/4 = a₁(-2)⁵

 

                           a₁ = -37/128

 

a₁₃ = a₁r¹² = (-37/128)(4096) = -1184