ACM 3 / Math 4 SEQUENCES & SERIES TEST REVIEW

1. For each of the following sequences,

a) find a possible formula for an

b) use your formula to find a21, express your answer in exact values only

i) 6, 18, 54, … ii) 4/5 , 7/25, 10/125 ,….

iii) 25, 16, 9, 4, …

2. The Italian mathematician Leonardo Fibonacci developed a mathematical system to describe a rabbit population. The Fibonacci sequence is the recursive sequence where the first two terms have a value of 1 and each successive term is the sum of the two previous terms.

a) Use the above information to write a recursive formula for the Fibonacci sequence.

b) List the first ten terms of the sequence. Steps need not be shown.

3. If the terms 27, x, y, 8 form a geometric sequence, find x and y.

4. Student Council is going to sell tickets for a candy-give-away. Each person who buys a $5 ticket will have his/her name put into a lottery. All the names will be drawn – the first person will receive 1 candy, the second person receives 2 candies, the third 4 candies, the fourth 8 candies, and so on. Student Council predicts that they will sell 25 tickets.

a) How many candies will the 25th person receive?

b) How many candies will Student Council need altogether for 25 tickets?

c) If the cost is $1 for 1000 candies, what profit/loss will Student Council make from this

fundraiser?

5. Determine the sum of the series 88+ 83 + 78 + …+33 .

6. The sixth term of a geometric sequence is 10 and the tenth term is 160.

a) Find the possible values for the first term and the common ratio.

b) Use your values in (a) to determine t13 of the sequence.

7. The second term of an arithmetic series is 10 and the sum of the first 18 terms is 1125.

Find the common difference.

8.You start a dot-com business. Like all dot-com businesses, it starts great, and then starts going downhill fast. Specifically, you make $10,000 the first day. Every day thereafter, you make $200 less than the previous day—so the second day you make $9,800, and the third day you make $9,600, and so on. You might think this pattern stops when you hit zero, but the pattern just keeps right on going—the day after you make $0, you lose $200, and the day after that you lose $400, and so on.

  • a. If n is the day, and d is the amount of money you gain on that day, is the list of all d numbers an arithmetic sequence, geometric, or neither?
  • b. How much money do you make on the 33rd day?
  • c. On the day when you lose $1,000 in one day, you finally close up shop. What day is that?
  • d. Your accountant needs to figure out the total amount of money you made during the life of the business. Express this question in summation notation.

9.A geometric series has a 1 = 8 and a 2 = 24

  1. Find the common ratio.
  1. Find a 30.
  1. Find n if a n = 216 (Hint: solve the exponential equation using logarithms)
  1. Find S5.

e. Find the limit (sum) of the infinite seriesSn if it exists

10. Calculate:

11. Calculate:

12. The fourth term of a geometric sequence is 125, and the 10th term is 125/64. Find the

14th term. (Assume that the terms of the sequence are positive).

13. If the product of the first three terms of a geometric sequence is 3375, and the first

term is 5 find the common ratio and the second and third terms.

14. Find the 7th term of the sequence 7, 21, 63 . . .

15. Write the first five terms of the arithmetic sequence if the fourth term is 16 and the

tenth term is 46.

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