Question

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

Answer 1

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.