Arithmetic Progressions - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress

Transcript

Arithmetic Progressions In an Arithmetic Progression (AP), difference between two terms is constant Here, First term = a = 3 Common Difference = d = 5 − 3 = 2 Let’s do another example Growing Pattern of Squares Here, Number of squares are increasing Counting number of squares, we get 1, 5, 9, 13, …. We notice that the number of squares are increasing by 4 in each step Since they are increasing by the same number We can say that Difference between two successive terms is the same, so it is an AP But, how do we find number of squares in Stage 5? Stage 6? Stage 100? We know that our AP is 1, 5, 9, 13, … Here, First term = a = 1 Common difference = d = 5 – 1 = 4 Thus, we can write Number of squares in Stage 5 = Number of Saures in Stage 4 + Common difference = 13 + 4 = 17 And, Number of squares in Stage 6 = Number of Saures in Stage 5 + Common difference = 17 + 4 = 21 But, how do we find Number of squares in Stage 100? We cannot find all Squares from Stage 1 to 99 to find 100, we need a formula Let’s look the formula Thus, we can write Number of squares in Stage 5 = Number of Saures in Stage 4 + Common difference = 13 + 4 = 17 And, Number of squares in Stage 6 = Number of Saures in Stage 5 + Common difference = 17 + 4 = 21 But, how do we find Number of squares in Stage 100? We cannot find all Squares from Stage 1 to 99 to find 100, we need a formula. Let’s look the formula