8adv.MATH.12.E

Write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms.

Grade 8 (Advanced) · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
formulanth termarithmetic sequencesgeometric sequencesterms
Skills
  • write (a formula for the nth term of arithmetic sequences given several terms) #dok2
  • write (a formula for the nth term of geometric sequences given several terms) #dok2
  • analyze (patterns in sequences to identify arithmetic or geometric relationships) #dok2
  • use (formulas to generate additional terms in a sequence) #dok1
Learning Targets
  • I can use a pattern in a sequence to determine if it is arithmetic or geometric. #dok1
  • I can use a provided arithmetic sequence to find the formula for the nth term. #dok2
  • I can use a provided geometric sequence to find the formula for the nth term. #dok2
  • I can analyze several terms of a sequence to identify whether the relationship is arithmetic or geometric. #dok2
  • I can generate additional terms in a sequence once I have found the formula. #dok1
Big Ideas
  • Arithmetic and geometric sequences can be described with formulas that predict any term in the sequence.
  • Recognizing patterns in given terms allows us to derive a formula that can be used to extend sequences and solve real-world problems.
Essential Questions
  • How can I distinguish between arithmetic and geometric sequences given several terms?
  • What strategies can I use to identify a formula for the nth term of an arithmetic or geometric sequence?
  • How does knowing the formula for the nth term of a sequence help in solving problems or making predictions?
  • What information is necessary to write the nth-term formula for a sequence?
  • How do patterns and relationships within sequences connect to functions and algebraic thinking?