Question

What is the common difference of the arithmetic sequence 50, 46, 42, 38,....?
Answer
wrong lol
Answer
Determine the 6th and 20th terms of the arithmetic sequence above.
Answered by GPT 3.5
The common difference of an arithmetic sequence is the difference between any two consecutive terms.

In this case, the common difference can be found by subtracting any two consecutive terms in the sequence.

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

Therefore, the common difference of the sequence 50, 46, 42, 38,... is -4.
Answered by GPT 3.5
I apologize for my mistake. Let me correct that.

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

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

The common difference of the sequence 50, 46, 42, 38,... is -4.
Answered by GPT 3.5
To find the 6th term of an arithmetic sequence, we can use the formula:

\[a_n = a_1 + (n-1)d\]

Where:
- \(a_n\) is the nth term of the sequence
- \(a_1\) is the first term of the sequence
- \(n\) is the term number
- \(d\) is the common difference

Given that the first term, \(a_1 = 50\), the common difference, \(d = -4\), and we need to find the 6th term:

For the 6th term:
\[a_6 = 50 + (6-1)(-4)\]
\[a_6 = 50 + 5(-4)\]
\[a_6 = 50 - 20\]
\[a_6 = 30\]

Now, let's find the 20th term using the same formula:

For the 20th term:
\[a_{20} = 50 + (20-1)(-4)\]
\[a_{20} = 50 + 19(-4)\]
\[a_{20} = 50 - 76\]
\[a_{20} = -26\]

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