8/8/2019 Arithmetic Mon

1/2

CHAPTER 1: PROGRESSIONS Sri Sarjana Tuition Centre Add Maths Form 5

It's okay to make mistakes. Mistakes are our teachers -- they help us to learn ~ John Bradshaw 1

Arithmetic Progression

Examples

1. In each of the arithmetic progression below find (i) the commondifference, (ii) the 15th term.(a) 102, 99, 96,..(b) ,.....3

8,

3

7,

3

6,

3

5

2. Find the 16th term of the arithmetic progression,.......3,

3

21,

3

1

3. Find the nth term of the arithmetic progression,......9,

2

1,6,4

4. Find the number of terms of the arithmetic progression:4, 1, 2, , 44

5. Find the number of the multiples of 3 between 20 and 220.6. The first three terms of an arithmetic progression are 3x 1, 4x + and 3 2x. Find the value ofx.7. Given that kkk 42,12,4 2 are three consecutive terms of an A.P., find the possible values ofk.8. [SPM 2010,P1,4M] The first three terms of an arithmetic progression are 3h, k, h + 2.

(a) Express kin terms ofh.(b) Find the 10th term of the progression in terms ofh.

9. The 12th term and the 17th term of an A.P. are 38 and 53 respectively. Find the second term.10. For the arithmetic progression 184, 181, 178,.., find the value of the first negative term.11.

8 cm

The above figure shows a series of isosceles triangles with a constant height of 8 cm. The base of the first

triangle is x cm and the base of each of the following triangles increases by 2 cm, in sequence. Show that theareas (in cm

2) of the series of triangles form an arithmetic progression. Hence, state the commondifference.

dnaTn n )1(,th termThe !

2312 TTTT !

cmx cm2x cm4x

aT !1

,

irst termThe

1,di

erencecommonThe

!nn

TTd

8/8/2019 Arithmetic Mon

2/2

CHAPTER 1: PROGRESSIONS Sri Sarjana Tuition Centre Add Maths Form 5

It's okay to make mistakes. Mistakes are our teachers -- they help us to learn ~ John Bradshaw 2

12. Find the sum of the first 15 terms of the arithmetic progression,......4,7,10

13. Find the sum of the first n terms of the arithmetic progression 11, 7, 3,.14. For the arithmetic progression4, 1, 6,, find the sum of all the terms from the 8th term to the 20th term.15.

Find

the sum of all the terms of the arithmetic progressio

n

14,.......,4

32,

2

11,

4

1.

16. How many terms of the arithmetic progression 12, 16, 30,.. must be taken for the sum to be equal to 132?17. The second term of an arithmetic progression is 8 while the sum of the first six terms is 30. Find the common

difference.

18. In an A.P., the 4th term exceeds the 8th term by 12. The sum of the first 10th terms is equal to 25.(a) Find the first term and the commondifference of the progression.(b) Hence, find the sum of the first 8th terms after the 10th term of the progression.[Ans: (a) a = 16, d= 3 (b) 196]

19. The first two terms in an arithmetic progression are 5 and 9. The last term in the progression is the only termwhich is greater than 200. Find the sum of all the terms in the progression. [Ans: 5150]

20.

The diagram shows a part of the arrangement of circular tiles of equal size commented on wall. The number of

tiles in the lowest row is 108. In each of the other rows above, the number of tiles is 2 less than that in the row

below it. The diameter of each tile is213 cm. If the number of tiles in the highest row is 14, calculate

(a) the height, in cm, of the wall covered by the tiles,(b) the total surface area, in cm2, covered by the tiles.[Take

7

22!T ][Ans: (a) 168 cm (b) 281 182 cm

2]

Exercises

? Adnan

Sn )1(22

!

? AN! an

Sn2

1

nnnSS

y y y y y y y y

y y y y y y y y

y y y y y y y y