We have arithmetic sequences.
(i) 9; 14; 19; ...
a1=9,a2=14,a3=19,a4=24,a5=29,...
The common difference: d=a2−a1=14−9=5.
The general term: an=a1+d(n−1)=9+5(n−1).
(ii) 3; 7; 11; ...
a1=3,a2=7,a3=11,a4=15,a5=19,...
The common difference: d=a2−a1=7−3=4.
The general term: an=a1+d(n−1)=3+4(n−1).
(iii) 8; 15; 22; ...
a1=8,a2=15,a3=22,a4=29,a5=36,...
The common difference: d=a2−a1=15−8=7.
The general term: an=a1+d(n−1)=8+7(n−1).
(iv) 4 ; 11; 18; ....
a1=4,a2=11,a3=18,a4=25,a5=32,...
The common difference: d=a2−a1=11−4=7.
The general term: an=a1+d(n−1)=4+7(n−1).
(v) The number sequence of positive multiples of three starting at six:
6; 9; 12; 15; ...
a1=6,a2=9,a3=12,a4=15,a5=18,...
The common difference: d=a2−a1=9−6=3.
The general term: an=a1+d(n−1)=6+3(n−1).
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