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## 5.6.3 Progressions, SPM Practice

Question 5: Diagram 1 shows four rectangles. The largest rectangle has a length of L cm and a width of W cm. The measurement of the length and width of each subsequent rectangle are half of the measurements of its previous one. The areas of the rectangles form a geometric progression. The terms of the … Read more

## 5.6.2 Progressions, SPM Practice

Question 3: An arithmetic progression has 16 terms. The sum of the 16 terms is 188, and the sum of the even terms is 96. Find (a) the first term and the common difference, (b) the last term. Solution: (a) Let the first term = a Common difference = d Given    S 16 =188 … Read more

## 5.6.1 Progressions, SPM Practice (Paper 2)

Question 1: Diagram below shows part of an arrangement of bricks of equal size. The number of bricks in the lowest row is 100. For each of the other rows, the number of bricks is 2 less than in the row below. The height of each brick is 7 cm. Rahman builds a wall by … Read more

## 5.5.3 Geometric Progressions, SPM Practice (Paper 1)

Question 11: Express the recurring decimal 0.187187187 … as a fraction in its simplest form. Solution: Question 12: Given that  1 p =0.1666666…..  =q+a+b+c+….. where p is a positive integer. If q = 0.1 and a + b + c are the first three terms of a geometric progression, state the value of a, b and … Read more

## 5.5.2 Geometric Progressions, SPM Practice (Paper 1)

Question 6: The first three terms of a sequence are 2, x, 18. Find the positive value of x so that the sequence is (a) an arithmetic progression, (b) a geometric progression. Solution: Question 7: Given a geometric progression 2 z , 3,  9z 2 , q,…. express q in terms of z. Solution: Question 8: The … Read more

## 5.5.1 Geometric Progressions, SPM Practice (Paper 1)

Question 1: The fourth term of a geometric progression is –20. The sum of the fourth and the fifth term is –16. Find the first term and the common ratio of the progression. Solution: Question 2: The fourth and the seventh terms of a geometric progression are 18 and 486 respectively. Find the third term. … Read more

## 5.4.4 Sum to Infinity of Geometric Progressions

5.4.4 Sum to Infinity of Geometric Progressions (G) Sum to Infinity of Geometric Progressions S ∞ = a 1 − r , − 1 < r < 1 a = first term r = common ratio S∞ = sum to infinity Example: Find the sum to infinity of each of the following geometric progressions. (a) 8, 4, … Read more

## 5.4.3 Sum of the First n Terms of a Geometric Progression

5.4.3 Sum of the First n Terms of Geometric Progressions (F) Sum of the First n Terms of Geometric Progressions S n = a ( r n − 1 ) r − 1 , r > 1 S n = a ( 1 − r n ) 1 − r , r < 1 a = first … Read more

## 5.4.2a The nth Term of Geometric Progression (Examples)

Example 1: The sixth term of a geometric progression is 32 and the third term is 4. Find the first term and the common ratio. Smart TIPS: Solving the simultaneous equation of a and r. Using the formula T n = a r n−1 Solution: T 6 =32 a r 5 =32 —– (1) T 3 =4 a r 2 =4 —– (2) (1) (2) = a r 5 a … Read more

## 5.4.2 The nth term of a geometric progression

5.4.2 The nth Term of Geometric Progressions (C) The nth Term of Geometric Progressions T n = a r n − 1 a = first term r = common ratio n = the number of term Tn = the nth term Example 1: Find the given term for each of the following geometric progressions. (a) 8 … Read more