jmc

Question

Given that the third term of a geometric sequence is 1053 and the ninth term is 139, find the value of the seventh term.

Accepted Answer

Since ar^2=1053 and ar^8= 139, dividing the two terms allows us to solve for the common ratio r: r^6= ar^8ar^2=1729.Thus, r=13 and the seventh term equals ar^6=ar^8r^2= 13/91/9=13.