Question

What is the common difference d of the sequence?

Answer 1

Answer:

Question 1) Option 1

Question 2) Option 1

Question 3) Option 3

Question 4) Option 1

Question 5) Option 1

Step-by-step explanation:

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

Question 2) If a sequence is $a_{n} = 25- 3n$

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

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

$a_{n}= 15.5 + (13-15.5)n$

$a_{n} = 15.5 -2.5n$

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 $a_{1} = 195$ and common difference of the sequence is 16.

The sequence will be $a_{n}= 195 + nd = (195 + 16n)$

After 12th week number of cards will be

$a_{12}= 195 + (12)(16) = 195 + 192 =387$

So option 1 is correct.

Question 5) If the sequence is $a_{n} = 4n-1$

Then $a_{1} = 4(1)-1 =(4-1) =3$

and $a_{2} = 8-1 = 7$

Common difference will be 7-3 =4

Therefore $a_{n}= a_{n-1}+4$

Option 1. is the correct answer.