Question

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

Answer 1

I will rename them as
a , ar, and ar^2

given: ar = a+4
ar^2 = ar+9

ar^2 = a+4 + 9 = a + 13

but we also know that ar^2/ar = ar/a
using the property of common ratio

(a+13)/(a+4) = (a+4)/a
a^2 + 13a = a^2 + 8a + 16
5a = 16
a = 16/5

common ratio = ar/a = (a+4)/a
= (16/5 + 4)/(16/5)
= 9/4

terms are :
16/5 , 36/5 , 81/5

check:
T1 + 4
= 16/5+4 = 36/5 which is T2
T2 + 9
= 36/5 + 9 = 81/5 which is T3

my answer is correct