# Biology Exercise

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TUTORIAL 3 SEQUENCES AND SERIES

3.1 Sequences and Series

1. Find the first four terms and 100th term of the sequence.
(a) [pic] (b) [pic] (c) [pic]

2. Find the nth term of a sequence whose first several terms are given.
(a) [pic]…… (b) 0, 2, 0, 2, 0, 2 ……

3. Find the sum.
(a) [pic] (b) [pic]

4. Write the sum using sigma notation.
(a) [pic]

(b)[pic]

5. Find the nth term for each of the following sequences. Hence, determine whether the respective sequence is divergent or convergent. For a convergent sequence, state its limits. [pic]

[pic]

6. For the sequence [pic]find the nth term and show that the above sequence is convergent and determine its limits.

7. The tenth term of an arithmetic sequence is [pic], and the second term is [pic]. Find the first term.

8. The first term of an arithmetic sequence is 1, and the common difference is 4. Is 11937 a term of this sequence? If so, which term is it?

9. The common ratio in a geometric sequence is [pic], and the fourth term is [pic]. Find the third term.

10. Which term of the geometric sequence 2, 6, 18, … is 118098?

11. Express the repeating decimal as fraction.
(a) 0.777… (b) [pic] (c) [pic]

12. Find the sum of the first ten terms of the sequence.
[pic]

13. The sum of the first three terms of a geometric series is 52, and the common ratio is r = 3. Find the first term.

14. A person has two parents, four grandparents, eight great-grandparents, and so on. What is the total number of a person’s ancestors in 15 generations.

15. Find the sum of infinite geometric series.
(a) [pic]

(b) [pic]

16. The nth term of an arithmetic progression is [pic]. Find the first two terms and also the common difference of the arithmetic progression.

17. (i) Find the sum of the positive integers less than 100 which are multiples of 3 or...

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