Progressions

2. Geometric Progression (A) Characteristics of Geometric Progressions  Geometric progression is a progression in which the ratio of any term to the immediate term before is a constant. The constant is called common ratio, r. Example: Determine whether or not each of the following number sequences is a geometric progression (GP). (a) 1, 4, 16, … Read more

Question 11: An arithmetic progression consists of 10 terms. The sum of the last 5 terms is 5 and the fourth term is 9. Find the sum of this progression. Solution: Question 12: The sum of the first 6 terms of an arithmetic progression is 39 and the sum of the next 6 terms is … Read more

Question 6: Find the number of the multiples of 8 between 100 and 300. Solution: Question 7: Find the sum of all the multiples of 7 between 100 and 500. Solution: Question 8: If log 10 p,  log 10 pq and  log 10 p q 2 are the first three terms of a progression, show that … Read more

Question 1: The third and eighth terms of an arithmetic progression are –5 and 15 respectively. Find (a) The first term and the common difference (b) The sum of the first 10 terms. Solution: (a) T 3 =−5   → Use  T n =a+( n−1 )d a+2d=−5→( 1 ) T 8 =15 a+7d=15→( 2 ) ( 2 )−( … Read more

5.2.3 Sum of the First nTerms of an Arithmetic Progression  (F) Sum of the First n terms of an Arithmetic Progressions S n = n 2 [ 2 a + ( n − 1 ) d ] S n = n 2 ( a + l ) a = first term d = common difference … Read more

The nth Term of Arithmetic Progression (Examples)   Example 1: If the 20th term of an arithmetic progression is 14 and the 40th term is –6,  Find (a) the first term and the common difference, (b) the 10th term.   Solution: (a) T20 = 14 a + 19d = 14 —– (1) ← (Tn = … Read more

5.2.2 The nth term of an Arithmetic Progression (C) The nth term of an Arithmetic Progression   Tn = a + (n − 1) d where a = first term d = common difference n = the number of term Tn  = the nth term (D) The Number of Terms in an Arithmetic Progression Smart TIPS: You … Read more

Progression 5.2.1 Arithmetic progression(A) Characteristics of Arithmetic Progression An arithmetic progression is a progression in which the difference between any term and the immediate term before is a constant.  The constant is called the common difference, d.  d = Tn – Tn-1   or  d = Tn+1 – Tn Example 1:  Determine whether the following number … Read more