Part A
What is the common difference of the arithmetic sequence 50, 46, 42, 38,....?
(1 point)
Responses
4
4
-3
-3
-4
-4
2
2
Question 2
Part B
Determine the 6th and 20th terms of the arithmetic sequence above.
(2 points)
6th term is
20th term is
Part A:
The common difference of the arithmetic sequence is -4.
Part B:
To find the 6th term, we use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n-1)d
Where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference.
So, the 6th term is:
a_6 = 50 + (6-1)(-4)
a_6 = 50 + 5(-4)
a_6 = 50 - 20
a_6 = 30
The 6th term is 30.
To find the 20th term, we use the same formula:
a_20 = 50 + (20-1)(-4)
a_20 = 50 + 19(-4)
a_20 = 50 - 76
a_20 = -26
The 20th term is -26.