Step-by-step explanation:
a. The rule is to add 3 to each corresponding term.
Multiply 3 by 9 and 20, then add to 7;
[tex]3 \times 9=27+7=34 \checkmark[/tex]
[tex]3\times20=60+7=67 \checkmark[/tex]
b. The rule is to subtract [tex]-2\frac{1}{2}[/tex].
Multiply [tex]-2\frac{1}{2}[/tex] by 9 and 20, then add 2;
[tex]-2\frac{1}{2} \times 9=-22\frac{1}{2}+2=-20\frac{1}{2} \checkmark[/tex]
[tex]-2\frac{1}{2} \times 20=-50+2=-48 \checkmark[/tex]
c. The rule is to add 1 to the whole number and add 2x to the coefficient.
Multiply 1 and 2x by 9 and 20, then add 4 and 7x;
[tex]1\times9=9+4=13\\2x\times9=18x+7x=23x\\13+23x \checkmark[/tex]
[tex]1\times20=20+4=24\\2x\times20=40x+7x=47x\\24+47x \checkmark[/tex]
d. The first term is -2, and the rule is to multiply by [tex]3\frac{3}{5}[/tex].
Multiply [tex]3\frac{3}{5}[/tex] by 9 and 20, then subtract 2;
[tex]3\frac{3}{5} \times 9 =32\frac{2}{5}-2=30\frac{2}{5} \checkmark[/tex]
[tex]3\frac{3}{5} \times 20=72-2=70 \checkmark[/tex]
e. The first term is 5, and the rule is to multiply by 1.
10th and 21st terms: [tex]5 \checkmark[/tex]
