Question

Find the sixth term of a geometric sequence with t5=24 and t8=3

Answer 1

Hello,


`t_(2)=t_(1)*q\\ t_(3)=t_(2)*q=t_(1)*q^(2)\\ ...\\ t_(5)=t_(1)*q^(4)\\ t_(8)=t_(1)*q^(7)\\\\ (3)/(24)= (1)/(8)=(t_(8))/(t_(5))= (t_(1)*q^(7))/(t_(1)*q^(4))=q^(3)\\ q= (1)/(2) \\ t_(6)=t_(5)*q=24* (1)/(2)=12\\`