What is the common difference d of the sequence?

-15, -4, 7, 18, 29, ...

Question 1 options:

11

-11

12

-12

Question 2 (1 point)
What is the 8th term in the sequence?

an=25−3n
Question 2 options:

1

59

-6

22

Question 3 (1 point)
Which answer is the explicit rule for the sequence:

15.5, 13, 10.5, 8, 5.5, 3, ... ?

Question 3 options:

an=18+2.5n

an=18−2.5n

an=15.5−2.5n

an=15.5+2.5n
Question 4 (1 point)
Reggie has 195 trading cards in the first week. Each week, he purchases 16 more trading cards.

How many trading cards will he have in the 12th week?

Question 4 options:

387

371

-77

77

Question 5 (1 point)
What is the recursive rule for an=4n−1?

Question 5 options:

a1=3; an=an−1+4

a1=4; an=an−1−1

a1=3; an=an−1−1

a1=−1; an=an−1+4

Question 1) To calculate the common difference d of any sequence we subtract [tex]a_{n-1}[/tex] from [tex]a_{n}[/tex] for example [tex]a_{2}-a_{1}[/tex]=(-4) - (-15) = -4+15 = 11. Therefore option 1. (11) is the correct option for the sequence.

Question 2) If a sequence is [tex]a_{n} = 25- 3n[/tex]

Then the 8th term of the sequence will be [tex]a_{8}= 25 - 3(8)[/tex] = 25-24 = 1. So option 1 is correct.

Question 3) Explicit rule for any arithmetic sequence is [tex]a_{n}= a_{1} + (common difference)(n)[/tex]

[tex]a_{n}= 15.5 + (13-15.5)n[/tex]

[tex]a_{n} = 15.5 -2.5n[/tex]

Therefore option 3 is correct.

Question 4) Reggie has 195 cards in first week and 16 cards are added every week.

So from this question [tex]a_{1} = 195[/tex] and common difference of the sequence is 16.

The sequence will be [tex]a_{n}= 195 + nd = (195 + 16n)[/tex]

After 12th week number of cards will be

[tex]a_{12}= 195 + (12)(16) = 195 + 192 =387[/tex]

So option 1 is correct.

Question 5) If the sequence is [tex]a_{n} = 4n-1[/tex]

Then [tex]a_{1} = 4(1)-1 =(4-1) =3[/tex]

and [tex]a_{2} = 8-1 = 7[/tex]

Common difference will be 7-3 =4

Therefore [tex]a_{n}= a_{n-1}+4[/tex]

Option 1. is the correct answer.