Question

For a geometric sequence, t3 = 6 and ts = 2/81. Find t6

Answer 1

$$t_3=\dfrac{a}{b}$$

$$t_8=ar^7=\dfrac{2}{81}$$

$$\dfrac{t_8}{t_3}=\dfrac{ar^7}{ar^2}=r^5=\dfrac{\dfrac{2}{81}}{6}=\dfrac{1}{3^5 }$$

$$r=\dfrac{1}{3}$$

$$a(\dfrac{1}{3})^2=6=>a=54$$

$$t_6=54(\dfrac{1}{3})^5=\dfrac{2}{9}$$