Question 1 - Think & Reflect (Page 180) - Arithmetic Progressions - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress

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Question 1 - Think & Reflect (Page 180) Can you predict the number of squares in Stages 5 and 6 of the sequence? In Stages 10, 11 and 12? In Stage 20? At any stage? Here, Number of squares form an AP 1, 5, 9, 13, …. With First term = a = 1 Common difference = d = 5 – 1 = 4 Let’s find the Number of squares in different stages using our nth term of an AP formula an = a + (n − 1)d Now, Number of Squares in Stage 5 = 5th term = a5 = a + (5 – 1)d = a + 4d Putting values = 1 + 4 × 4 = 1 + 16 = 17 Number of Squares in Stage 6 = 6th term = a6 = a + (6 – 1)d = a + 5d Putting values = 1 + 5 × 4 = 1 + 20 = 21 Number of Squares in Stage 10 = 10th term = a10 = a + (10 – 1)d = a + 9d Putting values = 1 + 9 × 4 = 1 + 36 = 37 Number of Squares in Stage 11 = 11th term = a11 = a + (11 – 1)d = a + 10d Putting values = 1 + 10 × 4 = 1 + 40 = 41 Number of Squares in Stage 12 = 12th term = a12 = a + (12 – 1)d = a + 11d Putting values = 1 + 11 × 4 = 1 + 44 = 45 Number of Squares in Stage n = nth term = an = a + (n – 1)d Putting values = 1 + (n – 1) × 4 = 1 + 4n – 4 = 4n – 3