Topic Review — Growth and Decay in Sequences

← Growth and Decay in Sequences

This review covers arithmetic sequences, geometric sequences, growth and decay applications, and recurrence relations.

Review Questions

1. Find the 20th term of the arithmetic sequence 7, 12, 17, 22, …
2. Find the sum of the first 15 terms of the arithmetic sequence 3, 7, 11, 15, …
3. An arithmetic sequence has t₄ = 19 and t₉ = 44. Find a and d.
4. Find the 7th term of the geometric sequence 2, 6, 18, 54, …
5. Find the sum of the first 8 terms of the geometric sequence 1, 2, 4, 8, …
6. Is 135 a term in the geometric sequence 5, 15, 45, 135, …? Which term?
7. A population of 3 200 bacteria grows at 25% per hour. Find the population after 4 hours.
8. A car is purchased for $32 000 and depreciates at 18% per year. Find its value after 3 years.
9. Write the first 5 terms of the recurrence relation t_n+1 = t_n + 4, t₁ = 10. What type of sequence is this?
10. Write the first 5 terms of t_n+1 = 1.5t_n, t₁ = 8.
11. The recurrence relation t_n+1 = 1.06t_n − 3000, t₁ = 40 000 models a loan. Calculate t₂, t₃, and t₄.
12. An investment of $6 000 earns 4.5% per annum. In how many complete years will it exceed $8 000?
13. A geometric sequence has t₂ = 6 and t₅ = 48. Find a, r, and S₈.
14. A sequence is defined by t_n+1 = 0.9t_n + 50, t₁ = 500. Find the first 5 terms and determine the long-term (fixed point) value.
15. A theatre has 25 rows. Row 1 has 20 seats; each row has 2 more seats than the previous row. Find: (a) seats in row 25 (b) total seats in the theatre.