Question
The first term of an arithmetic sequence is -5, and the tenth term is 13. Find the common difference.
1.8
2
8/9
Answers
GPT 3.5
To find the common difference, we can 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 number of terms, and \(d\) is the common difference.
We are given that the first term (\(a_1\)) is -5, and the tenth term (\(a_{10}\)) is 13. Plugging these values into the formula, we get:
13 = -5 + 9d
Now we can solve for \(d\):
13 = -5 + 9d
18 = 9d
d = 18/9
d = 2
Therefore, the common difference is 2.
\(a_n = a_1 + (n-1)d\)
where \(a_n\) is the nth term, \(a_1\) is the first term, \(n\) is the number of terms, and \(d\) is the common difference.
We are given that the first term (\(a_1\)) is -5, and the tenth term (\(a_{10}\)) is 13. Plugging these values into the formula, we get:
13 = -5 + 9d
Now we can solve for \(d\):
13 = -5 + 9d
18 = 9d
d = 18/9
d = 2
Therefore, the common difference is 2.