Question

determine the geometric sequence if the second term is 1/9 and the sixth term is 1/729​

Answer 1

Step-by-step explanation:

Let a be the first term and r be the difference factor

so the general term equation would be something like

t(n)=a×r^(n-1)

so we know,

t(6)=a×r^5

and t(2)=a×r^1

dividing t6 by t2

t(6)/t(2)=(1/729)/(1/9)

(ar^5)/(ar)=1/81

r=1/3

substiting in t(2)

1/9=a×1/3

a=1/3

so now that we know "a" and "r" we can form the sequence which is

1/3,1/9,1/27,....