Question

Part A
What is the common difference of the arithmetic sequence 50, 46, 42, 38,....?

1. 4
2. 2
3. -4
4. -3

show work

Answer 1

To find the common difference of an arithmetic sequence, we subtract the second term from the first term.

46 - 50 = -4

Therefore, the common difference is -4.

3. -4

Answer 2

Part B

Determine the 6th and 20th terms of the arithmetic sequence above.

6th term is[ ]
20th term is[ ]

show work

Answer 3

To find the nth term of an arithmetic sequence, we use the formula:

an = a1 + (n-1)d

where:
an = the nth term
a1 = the first term
n = the term number
d = the common difference

Given:
a1 = 50
d = -4

6th term:
a6 = 50 + (6-1)(-4)
a6 = 50 + 5(-4)
a6 = 50 - 20
a6 = 30

Therefore, the 6th term is 30.

20th term:
a20 = 50 + (20-1)(-4)
a20 = 50 + 19(-4)
a20 = 50 - 76
a20 = -26

Therefore, the 20th term is -26.

6th term is 30
20th term is -26