SM (SAINS) SULTAN MAHMUDADDITIONAL MATHEMATICS

SPM ( 2005 – 2011 ) - Paper 1 - Progression

1. The second term of an arithmetic progression is –3 and the sixth term is 13.Find the first term and the common difference of the progression.

2. Diagram below shows three square cards.

Diagram 2

The perimeters of the cards form an arithmetic progression. The terms of the progression are in ascending order.

(a) Write down the first three terms of the progression.

(b) Find the common difference of the progression.

3. The 9th term of an arithmetic progression is 4 + 5p and the sum of the first four terms of the progression is 7p – 10, where p is a constant.Given that the common difference of the progression is 5, find the value of p.

4. The first three terms of an arithmetic progression are 46, 43 and 40.The nth term of this progression is negative.Find the least value of n.

5. Three consecutive terms of an arithmetic progression are 5 – x, 8, 2x.Find the common difference of the progression.

6. The sum of the first n terms of an arithmetic progression is given by .

Find

(a) the sum of the first 5 terms.

(b) the 5th term.

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7. The first three terms of an arithmetic progression are 3h, k, h + 2.

(a) Express k in terms of h.

(b) Find the 10th term of the progression in terms of h.

8. It is given that x, 5, 8, …, 41, …, is an arithmetic progression.

(a) State the value of x.

(b) Write the three consecutive terms after 41.

9. The first three terms of a geometric progression are x, 6, 12.

Find

(a) the value of x.

(b) the sum from the fourth term to the ninth term.

10. The first three terms of a geometric progression are 27, 18, 12.Find the sum to infinity of the geometric progression.

11. (a) Determine whether the following sequence is an arithmetic progression or a geometric progression.

16x, 8x, 4x, ...(b) Give a reason for the answer in (a).

12. In a geometric progression, the first term is 4 and the common ratio is r.Given that the sum to infinity of this progression is 16, find the value of r.

13. It is given that x2, x4, x6, x8, … is a geometric progression such that 0 < x < 1.

The sum to infinity of this progression is ..Find

(a) the common ratio of this progression in terms of x.

(b) the value of x.

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14. It is given that 1, x2, x4, x6, ... is a geometric progression and its sum to infinity is 3.

Find

(a) the common ratio in terms of x.

(b) the positive value of x.

15. The first three terms of a sequence are 2, x, 8.

Find the positive value of x so that the sequence is

(a) an arithmetic progression.

(b) a geometric progression.

16. The third term of a geometric progression is 16. The sum of the third term and the fourth term is 8.

Find

(a) the first term and the common ratio of the progression.

(b) the sum to infinity of the progression.

17.Given the geometric progression find the sum to infinity of the progression.

18. The sum of the first n terms of the geometric progression 8, 24, 72, ... is 8 744. Find

(a) the common ratio of the progression.

(b) the value of n.

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