Evaluate Exponential Sequence Rules
Written by Adi Ackerman, Head Teacher
"Evaluate Exponential Sequence Rules" is written for 8th Grade (Ages 13-14). A 7th grader who is already steady on algebra can use it too, and an older student can use it as a short review.
8th grade math worksheet: evaluate 12 geometric rules such as aₙ = −6 · 5^(n − 1) for terms like a_3 and a_5. Answer key included. Part of our sequence expressions algebra collection.
How do I use this worksheet?
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.
What students will practice
- Students will raise r to the power n − 1 before multiplying by the first term.
- Students will handle negative ratios such as −4 and fraction ratios such as 1/3.
- Students will find terms such as a_3, a_5 and a_7 from a geometric rule.
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FAQ
How do I use this sequence expressions worksheet?
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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.
What does this worksheet teach?
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Evaluate 12 geometric rules such as aₙ = −6 · 5^(n − 1) for terms like a_3 and a_5. The directions on the page read: Each rule gives the nth term of a geometric sequence. Find the terms named. Remember to raise r to the power n − 1 before you multiply. The page opens with a worked example, and an answer key is included.
Can I use this sequence expressions worksheet for homeschool or classroom?
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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.
How do you find a term from an nth term rule?
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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.
How do you write the nth term rule for an arithmetic sequence?
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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.
How do you find which term has a given value?
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Set the rule equal to the value and solve for n. For aₙ = −4n + 30 and the value −50, −4n = −80, so n = 20.
How do you evaluate a geometric sequence rule?
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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.
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