### Home > INT1 > Chapter 5 > Lesson 5.2.2 > Problem5-68

5-68.

Determine the common difference (sequence generator) for each arithmetic sequence listed below. Then write an equation for the $n^\text{th}$ term in each sequence, keeping in mind that the first term of each sequence is $t(1)$.

1. $4, 7, 10, 13, …$

$m = 3$

$7-4=10-7=13-10=3$

$t(n) = 3n + t(0)$
$t(1) = 3(1) + t(0) = 4$
$3 + t(0) = 4$
$t(0) = 1$

$t(n) = 3n + 1$

1. $3, 8, 13, …$

$m = 5$

$t(n)=5n-2$

1. $24, 19, 14, …$

$t(n)=-5n+29$

$m=-5$

1. $7, 9.5, 12, …$

$9.5-7=12-9.5=2.5$

$m = 2.5$

$t(0) = 4.5$

$t(n) = 2.5n + 4.5$