急!F6 Arithmetic Sequences 01q3

12 (a) 5T2-5T1=5(T2-T1)=5x3=15
5T3-5T2=5(T3-T2)=5x3=15
5T4-5T3=5(T4-T3)=5x3=15
..............
5Tn-5T(n-1)=5(Tn-T(n-1))=5x3=15
∴5T1, 5T2, 5T3, 5T4, ... is an arithmetic sequence.
The common difference=5T2-5T1=5(T2-T1)=5x3=15

12 (b) (5T2+c)-(5T1+c)=5(T2-T1)=5x3=15
(5T3+c)-(5T2+c)=5(T3-T2)=5x3=15
(5T4+c)-(5T3+c)=5(T4-T3)=5x3=15
.........................
(5Tn+c)-(5T(n-1)+c)=5(Tn-T(n-1))=5x3=15
∴5T1+c, 5T2+c, 5T3+c, 5T4+c, ... is an arithmetic sequence.
The common difference=(5T2+c)-(5T1+c)=5(T2-T1)=5x3=15

13(a) (T2-k)-(T1-k)=T2-T1=d
(T3-k)-(T2-k)=T3-T2=d
(T4-k)-(T3-k)=T4-T3=d
...................
(Tn-k)-(T(n-1)-k)=Tn-T(n-1)=d
∴T1-k, T2-k, T3-k, T4-k, ... is an arithmetic sequence.
The common difference=(T2-k)-(T1-k)=T2-T1=d

13(b) 2(T2-k)-2(T1-k)=2(T2-T1)=2d
2(T3-k)-2(T2-k)=2(T3-T2)=2d
2(T4-k)-2(T3-k)=2(T4-T3)=2d
.............................
2(Tn-k)-2(T(n-1)-k)=2(Tn-T(n-1))=2d
∴2(T1-k), 2(T2-k), 2(T3-k), 2(T4-k), ... is an arithmetic sequence.
The common difference=2(T2-k)-2(T1-k)=2(T2-T1)=2d

13(c) (T2-k/2)-(T1-k/2)=T2-T1=d
(T3-k/2)-(T2-k/2)=T3-T2=d
(T4-k/2)-(T3-k/2)=T4-T3=d
.....................
(Tn-k/2)-(T(n-1)-k/2)=Tn-T(n-1)=d
∴T1-k/2, T2-k/2, T3-k/2, T4-k/2, ... is an arithmetic sequence.
The common difference=(T2-k/2)-(T1-k/2)=T2-T1=d