Exercise Question 1 (Page 178) - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress

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Exercise Question 1 (Page 178) Consider the expression 𝑡_𝑛=3𝑛−7. (i) Find its first, second, third, 12th, 18th and 50th terms. (ii) Which term of the sequence is 332? (iii) Is 557 a term of this sequence? Why or why not? Let’s answer this one-by-one (i) Find its first, second, third, 12th, 18th and 50th terms. Now, First term = 𝑡_1 = 3(1)−7 = 3 – 7 = –4 Second term = 𝑡_2 = 3(2)−7 = 6 – 7 = –1 Third term = 𝑡_3 = 3(3)−7 = 9 – 7 = 2 12th term = 𝑡_12 = 3(12)−7 = 36 – 7 = 31 18th term = 𝑡_18 = 3(18)−7 = 54 – 7 = 47 50th term = 𝑡_50 = 3(50)−7 = 150 – 7 = 143 Now, we are asked (ii) Which term of the sequence is 332? We put 𝑡_𝑛 = 332 and find value of n Second term = 𝑡_2 = 3(2)−7 = 6 – 7 = –1 Third term = 𝑡_3 = 3(3)−7 = 9 – 7 = 2 12th term = 𝑡_12 = 3(12)−7 = 36 – 7 = 31 18th term = 𝑡_18 = 3(18)−7 = 54 – 7 = 47 50th term = 𝑡_50 = 3(50)−7 = 150 – 7 = 143 Now, we are asked (ii) Which term of the sequence is 332? We put 𝑡_𝑛 = 332 and find value of n Also, we are asked (iii) Is 557 a term of this sequence? Why or why not? If n is a natural number, then 557 is a term of sequence If n is in fractions, then 557 is not a term of the sequence Let’s do that 𝑡_𝑛 = 557 3n – 7 = 557 3n = 557 + 7 3n = 564 n = 564/3 n = 188 Since n is a natural number, ∴ 557 is a term of the sequence