Question

The first three term 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

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

r = 9/4
a = 16/5

so, now figure the first 3 terms.

Answer 2

let the first 3 terms be
a , ar , and ar^2

ar = a + 4
ar - a = 4
a(r-1) = 4
a = 4/(r-1)

ar^2 = ar + 9
ar^2 - ar = 9
a = (9/(r^2 - r)

so 9/(r^2-r) = 4/(r-1)
4r^2 - 4r = 9r - 9
4r^2 - 13r + 9 = 0
(4r - 9)(r - 1) = 0
r = 9/4 or r = 1

if r = 9/4,
a = 4/(9/4 - 1) = 16/5
<b>the first 3 terms are 16/5 , 36/5 , and 81/5</b>

if r = 1 , a = 4/0 , which would be undefined, so r≠1

a = 9/4, r = 16/5 yields the only solution


check:
first condition: t2 = t1 + 4
LS = 36/5
RS = 16/5 + 4 = 36/5 , check

2nd condition: t3 = t2 + 9
LS = 81/5
RS =36/5 + 9 =81/5 , check: