Question

1. Determine the 10th and 21st terms of each of the following arithmetic sequences

a) 7;10;13;.....

b) 2;
`- (1)/(2)`;-3;...​

c) 4+7x ; 5+9x + 6+11x ;....

d) a= -2 ; Term(5)=18

e) a=5; Term(4)=4

Answer 1

Explanation:

a. The rule is to add 3 to each corresponding term.

Multiply 3 by 9 and 20, then add to 7;

`3 * 9=27+7=34 \checkmark`

`3*20=60+7=67 \checkmark`

b. The rule is to subtract
`-2(1)/(2)`.

Multiply
`-2(1)/(2)` by 9 and 20, then add 2;

`-2(1)/(2) * 9=-22(1)/(2)+2=-20(1)/(2) \checkmark`

`-2(1)/(2) * 20=-50+2=-48 \checkmark`

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;

`1*9=9+4=13\\2x*9=18x+7x=23x\\13+23x \checkmark`

`1*20=20+4=24\\2x*20=40x+7x=47x\\24+47x \checkmark`

d. The first term is -2, and the rule is to multiply by
`3(3)/(5)`.

Multiply
`3(3)/(5)` by 9 and 20, then subtract 2;

`3(3)/(5) * 9 =32(2)/(5)-2=30(2)/(5) \checkmark`

`3(3)/(5) * 20=72-2=70 \checkmark`

e. The first term is 5, and the rule is to multiply by 1.

10th and 21st terms:
`5 \checkmark`