if 2-5t;1-t;t+1 are the first 3terms of an infinite converging geometric sequence,determine the values of t

Answer 1

since r is constant,

(1-t)/(2-5t) = (t+1)/(1-t)

Solve that for t, and you will find that matching sequences are, with r=2 and r=1/3,

1/3, 2/3, 4/3, ...
9/2, 3/2, 1/2, ...