The first term of an arithmetic sequence is 4 and the tenth term is 67. What is the common difference?

The common difference of an arithmetic sequence can be found using the formula:<br /><br />\[ a_n = a_1 + (n-1)d \]<br /><br />where:<br />- \( a_n \) is the nth term,<br />- \( a_1 \) is the first term,<br />- \( n \) is the term number,<br />- \( d \) is the common difference.<br /><br />Given:<br />- \( a_1 = 4 \)<br />- \( a_{10} = 67 \)<br />- \( n = 10 \)<br /><br />We need to find \( d \). Plugging in the values, we get:<br /><br />\[ 67 = 4 + (10-1)d \]<br />\[ 67 = 4 + 9d \]<br />\[ 67 - 4 = 9d \]<br />\[ 63 = 9d \]<br />\[ d = \frac{63}{9} \]<br />\[ d = 7 \]<br /><br />So, the common difference is 7.