Exercise Question 2 (Page 182) - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress

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Exercise Question 2 (Page 182) (i) Using the formula 𝑡_𝑛=𝑎+(𝑛−1)×𝑑, find the nth term of the following arithmetic progressions. (i) 1/2, 5/2, 9/2, 13/2,… Here, First term = a = 𝟏/𝟐 Common difference = d = 5/2−1/2 = (5 − 1)/2 = 4/2 = 2 Now, nth term = 𝑡_𝑛 = a + (n – 1) × d Putting values = 𝟏/𝟐+(𝒏−𝟏) × 𝟐 = 1/2+2𝑛−2 = 2𝑛+(1− 2 × 2)/2 = 𝟐𝒏−𝟑/𝟐 = a + (n – 1) × d Putting values = 𝟏/𝟐+(𝒏−𝟏) × 𝟐 = 1/2+2𝑛−2 = 2𝑛+(1− 2 × 2)/2 = 𝟐𝒏−𝟑/𝟐 Exercise Question 2 (Page 182) (ii) Exercise Using the formula 𝑡_𝑛=𝑎+(𝑛−1)×𝑑, find the 𝑛^"th " term of the following arithmetic progressions. (ii) 1.5, 3.5, 5.5, 7.5,… Here, First term = a = 1.5 Common difference = d = 3.5 – 1.5 = 2 Now, nth term = 𝑡_𝑛 = a + (n – 1) × d Putting values = 1.5 + (n – 1) × 2 = 1.5 + 2n – 2 = 2n – 0.5 = 1.5 + (n – 1) × 2 = 1.5 + 2n – 2 = 2n – 0.5