Answer to Question #122898 in Algebra for khomotso

Question

For each of the following number sequence below,
1.state the first term , and write the next four terms of the sequence
2. Find the common difference
3.find the general Th for the sequence
4.write down the input and output value of the five terms of the sequence in a table
5.represent the number sequence on a coordinate plane in a graphic form
6.write down the number sequence of positive multiples of three starting at six
7. 9;14,19;...
8. 3:7;11;....
9. 8;15;22;...
10. 4 ;11,18

Answer 1

We have arithmetic sequences.

(i) 9; 14; 19; ...

$a_1=9, a_2=14, a_3=19, a_4=24, a_5=29, ...$

The common difference: $d=a_2-a_1=14-9=5.$

The general term: $a_n=a_1+d(n-1)=9+5(n-1).$

(ii) 3; 7; 11; ...

$a_1=3, a_2=7, a_3=11, a_4=15, a_5=19, ...$

The common difference: $d=a_2-a_1=7-3=4.$

The general term: $a_n=a_1+d(n-1)=3+4(n-1).$

(iii) 8; 15; 22; ...

$a_1=8, a_2=15, a_3=22, a_4=29, a_5=36, ...$

The common difference: $d=a_2-a_1=15-8=7.$

The general term: $a_n=a_1+d(n-1)=8+7(n-1).$

(iv) 4 ; 11; 18; ....

$a_1=4, a_2=11, a_3=18, a_4=25, a_5=32, ...$

The common difference: $d=a_2-a_1=11-4=7.$

The general term: $a_n=a_1+d(n-1)=4+7(n-1).$

(v) The number sequence of positive multiples of three starting at six:

6; 9; 12; 15; ...

$a_1=6, a_2=9, a_3=12, a_4=15, a_5=18, ...$

The common difference: $d=a_2-a_1=9-6=3.$

The general term: $a_n=a_1+d(n-1)=6+3(n-1).$