Write nth Term Rules With Negative Differences

Begin with Evaluate Sequence Rules With Negative Terms, then Write the nth Term Rule. Use Write nth Term Rules From Tables and Graphs and From Word Problems for transfer, and the riddle or Match Sequences to nth Term Rules as review.

Write dn + c rules for 12 sequences with negative or fraction differences, such as 7 1/2, 7, 6 1/2, 6. The directions on the page read: Each list is an arithmetic sequence with a negative common difference d. Write a rule for its nth term in the form dn + c. Write fractions in simplest form. The page opens with a worked example, and an answer key is included.

Yes, both. We made it for 8th grade algebra, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

Replace n with the term number and simplify. For aₙ = −6n + 13, a_20 = −6 × 20 + 13 = −107. Evaluate Sequence Rules With Negative Terms has 14 rules to practice.

Find the common difference d, then find c by subtracting d from the first term. For −19, −13, −7, −1, d = 6 and c = −25, so aₙ = 6n − 25.

Set the rule equal to the value and solve for n. For aₙ = −4n + 30 and the value −50, −4n = −80, so n = 20.

Raise the ratio to the power n − 1 first, then multiply by the first term. For aₙ = −2 · (−3)^(n − 1), a_3 = −2 × 9 = −18.