Sequences &

SeriesRiddle Activity

Sequences & Series

Riddle Activity• Skills required (all for both arithmetic &

geometric):– Finding specific term of sequence– Finding explicit & recursive formula for a sequence

given first 4 terms– Finding the sum up to a given term number– Finding sum of infinite geometric series– Finding first term, last term, number of terms and sum

given sigma notation– Find formula, specific term and sum for a word problem

involving arithmetic sequence– Find specific term for a word problem involving

geometric sequence.• Activity is self-checking, as students will know

they did something wrong if they don’t see their answer right away!

• For each answer that students get, they will need to cross off their corresponding answer on the chart on the back. The remaining letters, when read left to right, row by row, will spell out the answer to the riddle. For each underlined thing inthe directions, students will have one box to cross off. See below for more direction:– #1-4: one box each– #5-6: two boxes each– #7-8: one box each– #9 & #11: two boxes each

- #10: one box- #12-13: 4 boxes each- #14a/b/c: one box each- #15: one box

Determine whether the following sequences are arithmetic or geometric. Then find the 10th term of the sequence.

1. 1536, , , ,… 2. , − , − ,− ,… 3. , , , , … 4. , 9 , , , …Find an explicit formula AND a recursive formula for each sequence.

5. . , . , , , … 6. , , , , …State whether each series is arithmetic or geometric, then find the sum up to the given term.

7. − + − + − + − +⋯ 𝑆 8. + + + +⋯ 𝑆

For each infinite geometric series, find the common ratio and state whether the series is convergent or divergent. If the series is convergent, then find the EXACT sum.

9. . − . + . − . +… 10. − + 9 − +⋯ 11. + + + +⋯

Why are Dasher & Dancer always

taking coffee breaks?

Name: Date: Period:

For each sum, identify the first term, the last term, and the number of terms. Then evaluate the sum. (Four items per question to find in the answers at the bottom.)

12. 13.

14. Tommy is trying out for basketball, so he decides to do practice his free-throws each day. On the first day, he shoots 4 free-throws and increases the number of free-throws

by 2 each day.

a. Write an explicit formula to model this situation.

b. How many free-throws will Tommy do on the 32nd

day?

c. Basketball tryouts are in 32 days, how many total free-throws will Tommy

have done by then?

15. Katy Perry put out a new song. The first day, the song was downloaded 4,502

times. Each day the downloads increase by 3%. Find out how many downloads she will

have after 3 weeks.

101

1

2 (5)k

k

13

3

17 3

2n

n

When you find your answer, cross it off. After you have completed all of the problems, read the

remaining letters row by row, starting on the top row to answer the riddle.

A. 𝑎 = T. = − diverges E. 𝑎 = , , R. 𝑎𝑛 = 𝑎𝑛− ∙ H. 𝑎 = −E. 𝑎𝑛 = ∙ . 𝑛−

F. = − diverges Y. , L. 𝑎 = M. 𝑎 =K. 𝑆 = − A. 𝑆 = . P. 𝑎 = − R. 𝑆 = − S. 𝑛 =E. 𝑎𝑛 = − 𝑛 + A. 𝑎 = S. 𝑛 = I. 𝑎𝑛 = 𝑛 − A. 𝑎 = −J. 𝑎 = N. 𝑎𝑛 = 𝑛 + T. , T. 𝑆 = , , , W. = .D. 𝑆∞ = . F. 𝑎 = A. 𝑎 = − L. 𝑎𝑛 = 𝑎𝑛− + S. 𝑆 = ,S. = − converges H. 𝑎𝑛 = 𝑛 + T. 𝑆 = A. 𝑎 = O. 𝑆 = , ,C. 𝑎𝑛 = . ∙ 𝑛− R. , B. 𝑎 = . V. = converges U. 𝑎 =C. 𝑆∞ = Y. 𝑆∞ = . U. 𝑆 = . K. 𝑆∞ = S. 𝑎 = −R. 𝑆 = S. = diverges C. = − converges E. 𝑛 =

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