急!F6 Arithmetic Sequences 01q2

17(a)
Tn+1 - Tn
=[2(n+1)+3] - (2n+3)
=(2n+5) - (2n+3)
=2
Tn is an a.s. with common difference 2.(b)
Tn+1 - Tn
=(n+1)^2-1 - (n^2-1)
= 2n+1
Tn is not an a.s. since 2n+1 is not a constant.(c)
Tn+1 - Tn
=(n+1)/3 -1 - (n/3 -1)
=1/3
Tn is an a.s. with common difference 1/3.
21(a)
99<=4n<=499
24.75<=n<=124.75
25<=n<=124
The number of multiples of 4 between 99 and 499 = 124-25+1=100.(b)
99<=6n<=499
16.5<=n<=83.166.......
17<=n<=83
The number of multiples of 6 between 99 and 499 = 83-17+1=67.(c)
The LCM of 4 and 6 is 12
99<=12n<=499
8.25<=n<=41.5833......
9<=n<=41
The number of multiples of 12 between 99 and 499 =41-9+1=33
So the number of common multiples of 4 and 6 =100+67-33=134.