modul jom tanya sifu_progressions@2014

8/13/2019 Modul Jom Tanya Sifu_Progressions@2014

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JOM TANYA SIFU@FORM 5

Chapter 1 : PROGRESSIONS


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CHAPTER 1 : PROGRESSIONS

PREPARED BY : PUAN HAYATI AINI BT AHMAD

1. The first three terms of an AP are 6, 10 and 14.Find(a) the first term(b) the common difference(c) the fifth term(d) the sum of the first 7 terms

2. The first three terms of an AP are 8, 4 and 0.Find(a) the first term(b) the common difference(c) the 8 th term(d) the sum of the first 10 terms

3. The first three terms of an AP are ,1 and 3.Find(a) the 16 th term(b) the sum of the first 6 terms

4. The first three terms of an AP are 3, and 2.Find(a) the 11 th term(b) the sum of the first eight terms

5. The first three terms of an AP are10, 7 and 4 . Find

(a) the 20 th term

(b) the sum of the first 12 terms

6. The first three terms of an AP are 5, 9 and 13.Find(a) the common difference(b) the sum of the first 20 terms


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1. The 7 th term and the 12 th term of an AP are 27and 47 respectively. Find the first term and thecommon difference.

2. The 12 th term and the 17 th term of an AP are 38and 53 respectively. Find the first term and thecommon difference.

3. The 13 th term of an AP is 27. Given that the 7 th term is 3 times the second terms, find the firstterm and the common difference.

4. The 8 th term of an AP is twice of the 2 nd term.The 11 th terms is 18. Find the first term and thecommon difference.

5. The first term of an AP is 4 . Given that thevalue of the 13 th term is 4 times the value ofthe 5 th term, find the common difference.

6. Given that the 10 th term of an AP is 33 and thedifference between the 8 th term and the 3 rd term is 15. Calculate the first term and thecommon difference.


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1. The first three terms of a GP are 3, -6, and 12.Find(a) the first term(b) the common ratio(c) the eighth term(d) the sum of the first 5 terms

2. The first three terms of a GP are 3, 6 and 12.Find(a) the first term(b) the common ratio(c) the 15 th term(d) the sum of the first 10 terms

3. The first three terms of a GP are

3, 2 and . Find(a) the 10 th term(b) the sum of the first 6 terms

4. The first three terms of a GP are 2, -6 and 18.Find(a) the 7 th term(b) the sum of the first 5 terms


,1 and 3 . Find(a) the fifth term(b) the sum of the first 15 terms


, and 2. Find(a) the common ratio(b) the sum of the first 6 terms


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1. In a GP, where all the terms are positive, thefourth term is 24 and the second term is 6.Calculate the first term and the common ratio.

2. If the second term of a GP is 3 and the seventhterm is , find the first term and the commonratio.

3. The third term and the sixth term of a GP are27 and 8 respectively. Find the first term andthe common ratio.

4. The second term and the third term of a GP are and 1 respectively. Find the first term and the

common ratio.

5. In a GP, the first term and the third termsexceeds the second terms by 12 and 24respectively. Find the first term and thecommon ratio.

6. In a GP, the sum of the second term and thethird term is 12 while the sum of the thirdterm and the fourth term is 6. Find thecommon ratio and the first term.


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1. The first three terms of an AP are 3, 3,2 2. Find

(a) the value of ,(b) the first term and the common difference

2. If 3 1,6 and 19 are three consecutiveterms in AP, find(a) the value of (b) the first term and the common difference

3. The first three terms of an AP are 6, 2 and -14. Find(a) the value of (b) the first term and the common difference

4. The first three terms of an AP are,2 2 and 2 1. Find

(a) the value of (b) the first term and the common difference

5. The first three terms of an AP are 4, 3 3,2 4. Find

(a) the value of ,(b) the sum of the first 10 terms of the

progression.

6. The 3 rd term and the 5 th term of an AP are2 6 and 6 4 respectively, where is aconstant. Given that the common difference ofthe progression is 3, find the value of .


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1. The first three terms of a GP are 5 , , . Findthe value of , given > 0.

2. The first three terms of a GP are 6, , 24. Findthe positive value of .



5. Given 36, , 4 are three consecutive terms of aGP with a negative common ratio. Find thevalue of .

6. The first three terms of a GP are 3, , 2.Find(a) the value of (b) the common ratio


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1. The first three terms of a GP are 3,6, . Find(a) the value of (b) the sum from the 6 th term to the 12 th term

2. The first three terms of a GP are 1, 4 ,8.Find(a) the value of (b) the sum from the 4 th term to the 7 th term

3. The first three terms of a GP are ,12,36. Find(a) the value of (b) the sum from the fifth term to the twelfth

term

4. The first three terms of a GP are positive. Giventhat the terms are 4, and 5 12. Find(a) the value of (b) the sum of the first 8 terms after the 5 th

term

5. The first three terms of a GP are 36, 12, 4. Find(a) the fourth term,(b) the sum of the first 10 terms after the

fourth term.

6. If 27,3 and 48 are three consecutive terms ina GP. Find(a) the values of (b) the sum of the first 7 terms after the

fourth term


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1. The first three terms of an AP are 4,3 3,2 4 . Find

(a) the value of (b) the sum of the first 10 terms after the 3 rd

term

2. The first three terms of an AP are 6, 10 and 14.Find(a) the common difference(b) the sum of the first 16 terms after the 4 th

term

3. The sum of the first n terms of an AP is givenby = [5 13].(a) the first term(b) the sum of the 6 th term to the 12 th term

4. It is given that 5, 11 and 17 are the first threeterms of an AP. Find(a) the tenth term(b) the sum of the next ten terms after the

tenth term.

5. The first three terms of an AP are 7, 11, 15.Find(a) the common difference(b) the sum of the first 30 terms after the

third term.

6. The first three terms of an AP are -3, 12 and 27.Find(a) the common difference(b) the sum of the first 18 terms after the 5 th

term


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1. The sum of first terms of an AP is given by = 2(9 ). Find

(a) the common difference(b) the sum of the first 6 terms

2. The sum of the first terms of an AP is givenby = 3 2 . Find(a) the common difference(b) the 10 th term.

3. The sum of the first terms of an AP is givenby = 2 5 . Find(a) the first term(b) the common difference

4. The sum of the first terms of an AP is givenby = (23 ). Find(a) the first term(b) the common difference

5. The sum of the first terms of a GP is given by = 2(3 1). Find

(a) the sum of the first 6 terms,(b) the 6 th term

6. The sum of the first term, , of a GP is given

by = 81 1 . Find(a) the common ratio(b) the sum to infinity


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1. The n th term of a GP is given by = 2 .Calculate(a) the common ratio(b) the sum to infinity

2. The n th term of a GP, , is given by

= + , find(a) the common ratio,(b) the sum to infinity

3. The n th term of a GP is given by = 7(3) .Calculate(a) the common ratio(b) the sum to infinity

4. The n th term of a AP, , is given by = 11 3 , find

(a) the common difference(b) the sum of the first 5 terms after the

fourth term

5. It is given that the n th term of a GP is = 3 Find(a) the common ratio(b) the sum of the first 6 terms

6. It is given that the n th term of a GP is = ( 3)

Find(a) the common ratio

(b) the sum of the first 10 terms after thethird term


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1. Express the recurring decimal 2.151515.. as afraction in its simplest form

2. Express the recurring decimal 1.020202 asa fraction in the lowest form.

3. Given = 0.1666666 = 0.1

(a) State the values of and of (b) Hence, find the value of

4. The recurring decimal 1.2333. can beexpressed as . Find the value of .

5. Given that 3.727272. = , find the value of and of

6. Given = 1.121212 is a recurring decimal,find the values of and of


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1. It is given that 46, 41,., z, 6,., is an AP (a) State the value of z(b) Write the three consecutive terms before z.

2. The fifth term of an AP is 6 and the sum of thefirst five term is 0. Find(a) the first term and the common difference(b) the sum of the first 12 terms

3. It is given that , , 2 , are the firstthree terms of an AP where the seventh termsis 74 and the sum of the first five terms is 290.Find the value of and of

4. The fourth term of an AP is 29 and the sum ofthe first eight terms is 260. Find(a) the first term and the common difference(b) the sum from the fourth term to the tenth

term

5. The sum of 14 terms in an AP is 224 and thesum of the odd terms is 105. Find the first termand the common difference of the progression.

6. An AP has 12 terms. The sum of 12 terms is192, and the sum of the odd terms is 90. Find(a) the first term and the common difference(b) the last term


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1. The first three terms of an AP are 49, 42 and35. The th term of this progression isnegative. Find the least value of

2. The first three terms of an AP are 89, 85 and81. The th term of this progression isnegative. Find the least value of

3. Given the sum of the first terms of an AP, 7,15, 23,, is greater than 3600. Find theminimum value of

4. Given that the AP 5, 9, 13,, find the value of terms of the progression is more than 500

for the first time.

5. The sum of the first terms of an AP is givenby = 2 5 . Calculate the value of thefirst term that exceeds the value of 500.

6. Given an AP 6, 18, 30, ..find the least numberof terms that must be taken so that its sumexceeds 864


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1. In the GP 4, 24, 144,, find the first termwhich exceeds 18 000.

2. In the GP 2, 6, 18,, find the least number ofterms required so that its sum exceeds 9 500.

3. Given a GP 2, 6, 18,, find the smallest value of such that the sum of the first terms is

greater than 6000

4. The first term and the common ratio of a GPare 100 and respectively. Find the smallestvalue of such that the sum of terms exceeds3 000

5. It is given that , 768, ,3 072,. Is part of aGP and the sum of the first four terms of theprogression is 255. Find(a) the common ratio(b) the first term

(c) the smallest value of such that the thterm exceeds 10 000

6. It is given that , 351, ,3 159,. Is part of aGP and the sum of the first six terms of theprogression is 4 732. Find(a) the common ratio(b) the first term

(c) the smallest value of such that the thterm exceeds 50 000

modul jom tanya sifu_progressions@2014

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