Maths question??

1.)480,240,120,60,30
The common ratio: 30
The 6th term:15

4,12,36,108,324
The common ratio:4
The 6th term:972

3.)Man is 7 years older than Shan ,and their total age is at least 51.Find their least possible ages.

let y be the age of Shan,
y+7 be the age of Man
y+y+7=51
2y=44
y=22
Man is 29 years old.
Shan is 22years old.

1.)
480,240,120,60,30
The common ratio:1/2
lets T(1)=480,T(2)=240,T(3)=120,...
T(2)/T(1)=1/2
T(3)/T(2)=1/2
...
so, ratio=1/2
The 6th term:15
T(n)=aR^(n-1)
if a=480,R=1/2
T(6)=(480)(1/2)^(6-1)
T(6)=15

4,12,36,108,324
The common ratio:3
lets T(1)=4,T(2)=12,T(3)=36,...
T(2)/T(1)=3
T(3)/T(2)=3
...
so, ratio=3
The 6th term:972
T(n)=aR^(n-1)
if a=4,R=3
T(6)=(4)(3)^(6-1)
T(6)=972

3.)Man is 7 years older than Shan ,and their total age is at least 51.Find their least possible ages.
T(n)=a+(n-1)d
if d=7, T(n)+T(n+1)>=51,
Man's ages -- T(n+1)=a+(n)7.....(1)
Shan's ages - T(n)=a+(n-1)7......(2)
(1)+(2),
2a+14n-7>=51
2(a+7n)>=58
a+7n>=29
if a+7n=29
T(n+1)=a+7n=29
T(n)=a+7n-7=22
so, Man's ages is 27, Shan's ages is 22