the first three terms of a geometric sequence are: t1; t2 and t3. if t2=t1-4 and t3=t2-9. determine the values of t1; t2 an t3

Answer 1

t1
r t1 = t1-4
r^2 t1 = (t1-4) -9 = t1 - 13

r (t1-4) = t1-13
r = (t1-13)/(t1-4) = (t1-4)/t1
so
t1^2 - 13 t1 = t1^2 -8 t1 + 16

-5 t1 = 16
t1 = -16/5 = -3.2

then r = (t1-4)/t1
= (-16/5 - 20/5)/-16/5 = 36/16 = 9/4

t2 = -16/5*9/4 = -7.2 = of course

t3 = -7.2*9/4 = -16.2 indeed -7.2-9