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

Question

(1 point)
Responses

4
4

-4
-4

2
2

-3
-3
Question 2
Part B

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

(2 points)
6th term is

20th term is

Answer 1

To find the common difference, we can subtract any two consecutive terms.

46 - 50 = -4
42 - 46 = -4
38 - 42 = -4

Therefore, the common difference is -4.

To find the 6th term:
6th term = first term + (n-1) * common difference
6th term = 50 + (6-1) * -4
6th term = 50 + 5 * -4
6th term = 50 - 20
6th term = 30

To find the 20th term:
20th term = first term + (n-1) * common difference
20th term = 50 + (20-1) * -4
20th term = 50 + 19 * -4
20th term = 50 - 76
20th term = -26

Therefore, the 6th term is 30 and the 20th term is -26.