For a given geometric sequence the 8th term a8 is equal to 4

For a given geometric sequence, the 8^th term, a_8, is equal to 47/25, and the 11^th term, a_11, is equal to -235. Find the value of the 14th term, a_14. If applicable, write your answer as a fraction.

Solution

a₈=47/25    a₁₁= -235

a_n=a r^n-1

a₈=a r⁷=47/25

a₁₁=a r¹⁰=-235

a₁₁/a₇= r¹⁰/r⁷= -235/47/25

        r³= -125

r=-5

a=47/25(-5^7)=-47/1953125

a₁₄= (-47/1953125)(-5)¹³= 29375