Answer Key 1

Assuming the first term of each sequence is n=1:
  1. \( a_n = 4-4n \) and \(a_{20} = -76\)
  2. \( a_n = \frac23(n-1)\) and \(a_{20} = \frac{38}{3}\)
  3. \(a_n = 36-11n\) and \(a_{20} = -184\)
  4. \( a_n= -5 + \frac72 n\)
  5. \( a_n=6 – \frac12 n\)
  6. \( a_n = -70+9n\)
  7. \( a_n = -5+9n\)
  8. \( a_n = 22-4n\)
  9. \(a_n = \frac{12}{5} – \frac25 n\)
  10. \( 2585\)
  11. \( n = 5\)
  12. \(a_n = 2\cdot 3^n\)
  13. \(a_n= \frac{15}{2} \cdot \left( \frac25 \right)^n \)
  14. \(a_n = 8 \cdot \left(\frac12\right)^n \)
  15. \(a_n = 60 \cdot \left(\frac12\right)^n \)
  16. \(a_n = -3072 \cdot \left( -\frac14\right)^n \)
  17. \(a_n = \frac45 \cdot 5^n \)
  18. \( a_n = \frac32 \cdot 2^n \) or \( a_n = \frac32 \cdot (-2)^n \)
  19. \( a_n = -160 \cdot 2^n\) or \(a_n = -160 \cdot (-2)^n\)
  20. \( a_n = 14\cdot \left(\frac12\right)^n\) or \(a_n = -14 \cdot \left(-\frac12\right)^n\)
  21. \( 5115 \) (Note, problem should read “…of the geometric series.”)

There’s also a chance that the teacher uses \( (n-1) \) more than \(n\) in the answers to 1-9 and 12-20. If so, then the teacher’s answers can be simplified into these answers.