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 and T3.
let those terms be a, ar and ar^2
T2 = T1 - 4 --> ar = a - 4
a(r-1)=-4
a = 4/(r-1)
T3 = T2 + 9
ar^2 = ar + 9
a(r^2 -r) = 9
a = 9/(r^2-r)
-4/(r-1) = 9/(r(r-1)(r+1))
-4 = 9/r
r = -9/4
then a = -4/(-9/4 - 1) = 16/13
the terms are:
16/13 , (16/13)(-9/4) , (16/13)(81/16)
= 16/13 , -36/13 , 81/13
check:
is there a common ratio ? yes
is T2 = T1-4 ? , YES
is T3 = T2+9 ? , YES