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ASSIGNMENT 1/ SEQUENCES / MAT 112

Inst. Profesional Baitulmal/ missb3nz

1. Given the progression ;32,...2

1,

4

1,

8

1Find

i. The sum of the first 6 terms.

ii. The number of the terms in the above progression.

2. Given the sequence 486, 162, 54, 18, Find

i. The 11th

term

ii. The sum of the first 9 term in the sequence.

3. The fourth and seventh term of arithmetic progression are 35 and 47 respectively. Find

the common difference and the first term.

4. i. How many terms of a sequence 9,12,15, are needed to make the sum

306?

ii. If )6(),9( + xx and 4 are the first three terms of a geometric progression,

find x.

5. Find the sum of the first 10 terms of the geometric progression: -9, -6, -4,

6. In an arithmetic sequence, the sum of the first ten terms is 125 and the third term is 5,

find the first term and the common difference.

7. The sum of the first and the third term of a geometric progression is2

13and the sum of

the third and the fifth term is8

117 . Find the common ratio and the first term given that

the common ratio is positive.

8. The fourth term exceeds the third term in a geometric progression by 54, and the sum of

the second and the third term is 36. Find the common ratio if it is positive.

9. How many terms of the progression 50, 46, 42, must be taken for the sum to be equal

to 0?

10. The second term of a geometric progression is larger than the first term by8

3but smaller

than the third term by16

9. Find the first three terms of the progression.

11. If the second term of a geometric progression is 5 and its fourth term is4

5, find its

seventh term if all the terms in the progression are positive.

12. If 18,8,3 +++ ppp are third, fourth and fifth term respectively of a geometric

progression. Find p

7/28/2019 Asg_1.pdf

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ASSIGNMENT 1/ SEQUENCES / MAT 112

Inst. Profesional Baitulmal/ missb3nz

13. The first term of an arithmetic progression is 9 and the last term is 279. The sum of the

progression is 2304. Find the common difference of the progression.

14. For the following sequence : 8, 4, 2, find

i. The 10th

term

ii. The sum of the first 12 terms

15. i. The sum of the first 15 terms of an arithmetic sequence is 600 and the

common difference is 5. Find the fourth term.

ii. Given the sequence 3, 1,3

1,

9

1, Find the sum of the first 10 terms.

16. Given a sequence : 2, 4, 8, ..., 2048. Find the number of terms in this sequence.

17. The second term and the sixth term of an arithmetic sequence are 85 and 105, respectively.

Find the common difference and the first term.

18. The first term of an arithmetic sequence is 5 and its last term is 40. If the common

difference is 1/4, find the number of terms in the sequence.

19. In a geometric sequence, the 7th term exceeds the 5th term by 48. Find the first term if thecommon ratio is 2.

20. In a drawing contest, all 16 participants will be given cash prizes as follows: RM725 for the

first winner, RM695 for the second winner, RM665 for the third winner, and so on.

Calculate the total amount of money awarded to all the participants.

21. In an arithmetic sequence, the sum of the first ten terms is 125 and the third term is 5. Find

(a) the first term and the common difference

(b) the sum of the first 15 terms.

22. An electrical appliances shop owner estimates that his sales will increase by 5% everymonth. The sales for the first month were RM30,000. Find

(a) the sales for the 10th month

(b) the total sales for the first year.

23. Given the sequence : 10, 8, 6 , , -24. Calculate

(a) the number of terms in the sequence

(b) the sum of the sequence.

24. Given the first three terms of Geometric Sequence: 2b+2, b+4, b,where each of the term ispositive, find:

(a) the value ofb.(b) the first term and common ratio.