In an arithmetic sequence, the first term, a subscript 1 is equal to 4, and the third term, a subscript 3 is equal to 14. Which number represents the common difference of the arithmetic sequence?
We can use the formula for the nth term of an arithmetic sequence to solve this problem. The formula is given by:
\[a_n = a_1 + (n-1)d\]
where \(a_n\) is the nth term, \(a_1\) is the first term, n is the position of the term, and d is the common difference.
Given that \(a_1 = 4\) and \(a_3 = 14\), we can substitute these values into the formula:
\[14 = 4 + (3-1)d\]
Simplifying:
\[14 = 4 + 2d\]
Subtracting 4 from both sides:
\[10 = 2d\]
Dividing both sides by 2:
\[5 = d\]
Therefore, the common difference of the arithmetic sequence is 5.