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?

Answer 1

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.