Question

Part A
What is the common difference between of the arithmetic sequence 50, 46 , 42, 38
1. 2
2. 4
3. -3
4. -4
Part B
Determine the 6th and 20th terms of the arithmetic sequence above

Answer 1

Part A:
To find the common difference between the terms of the arithmetic sequence 50, 46, 42, 38, we can subtract each term from the one before it.
46 - 50 = -4
42 - 46 = -4
38 - 42 = -4

Therefore, the common difference is -4.

Part B:
To find the 6th term of the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:

An = A1 + (n - 1)d

where:
An = the nth term
A1 = the first term
n = the term number
d = the common difference

For the 6th term:
A6 = 50 + (6 - 1)(-4)
A6 = 50 + 5(-4)
A6 = 50 - 20
A6 = 30

Therefore, the 6th term of the arithmetic sequence is 30.

To find the 20th term of the arithmetic sequence, we can use the same formula:

A20 = 50 + (20 - 1)(-4)
A20 = 50 + 19(-4)
A20 = 50 - 76
A20 = -26

Therefore, the 20th term of the arithmetic sequence is -26.