急! F6 Geometric Sequences 02q1

4(a) (i) First term T1=4x5^(1-1)=4x1=4
(ii) Second term T2=4x5^(2-1)=4x5=20
(iii) Common ratio=T2/T1=20/4=5

(b) (i) First term T1=3x2=6
(ii) Second term T2= 3x2^2=3x4=12
(iii) Common ratio=T2/T1=12/6=2

(c) (i) First term T1=2^(-1)=0.5
(ii) Second term T2 =2^(-2)=0.25
(iii) Common ratio=T2/T1=0.25/0.5=0.5

(d) (i) First term T1=-1/7
(ii) Second term T2=-1/7^2=-1/49
(iii) Common ratio=T2/T1=(-1/49)/(-1/7)=1/7

18. Test Second term:First term and Third term: Second term.
If the ratios are the same, then the sequence is a geometric sequence.

(a) First term T1=2^(1+1)=4
Second term T2=2^(2+1)=8
Third term T3=2^(3+1)=16
T2/T1=8/4=2
T3/T2=16/8=2
T2/T1=T3/T2
Therefore, the sequence is a geometric sequence.

(b) First term T1=3^(1(1+1))=3^2=9
Second term T2=3^(2(2+1))=3^6=739
Third term T3=3^(3(3+1))=531441
T2/T1=739/9=82.11...
T3/T2=531441/739=719.13...
T2/T1≠T3/T2
Therefore, the sequence is not a geometric sequence.

(c) First term T1=2^1x3^(1-1)=2x1=2
Second term T2=2^2x3^(2-1)=4x3=12
Third term T3=2^3x3^(3-1)=8x9=72
T2/T1=12/2=6
T3/T2=72/12=6
T2/T1=T3/T2
Therefore, the sequence is a geometric sequence.

(d) First term T1=5^(-1+1)=5^0=1
Second term T2=5^(-2+1)=5^(-1)=0.2
Third term T3=5^(-3+1)=5^-2=0.04
T2/T1=0.2/1=0.2
T3/T2=0.04/0.2=0.2
T2/T1=T3/T2
Therefore, the sequence is a geometric sequence.