1. Advanced Precalculus Notes 11.1 Sequences

2. A sequence is a function whose domain is the set of positive integers. Write the first six terms of the sequence: 1. Calculator notes: 2 nd Stat → OPS ↓ Seq((x-1)/x,x,1,6,1) 2.MODE →SeqTABLE SET (2 nd WINDOW)

3. Write and graph the first six terms of the sequence:

4. Write and graph the first six terms of the sequence:

5. Write the nth term of each sequence:

6. Write the first five terms of the sequence defined recursively by:

7. Write each sum in expanded form:

8. Write each sum using summation notation:

9. Find the sum of each sequence:

10. A trip will cost $450 and full payment is due March 2. To have the money, a student, on September 1, deposits $100 in a savings account that pays 4% per annum compounded monthly. On the first of each month, the student deposits $50. a) Find a recursive sequence for the account after n months. b) Find the amounts of the annuity for the first 6 months. c) After the deposit on March 1 is made, is there enough in the account to pay for the trip? d) If the student deposits $60 each month, will there be enough for the trip after the March 1 deposit?

11. Hayden borrowed $180,000 at 7% per annum compounded monthly for 30 years. The monthly payment is $1197.54. a) Find a recursive formula for the balance after each payment is made. b) What is the balance after the first payment? c) When will the balance be below $170,000?

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