Exercise Question 1 (Page 176)

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Exercise Question 1 (Page 176) Consider the sequence 1, 4, 7, 10, 13, … Can you predict the next four terms? Can you derive the first 10 terms of the sequence obtained by adding all the terms up to a given term of this sequence? Our sequence is 1, 4, 7, 10, 13, … Basically we add 3 to each term So, next four terms will be 13 + 3 = 16 16 + 3 = 19 19 + 3 = 22 22 + 3 = 25 Now, our next part of the question is Can you derive the first 10 terms of the sequence obtained by adding all the terms up to a given term of this sequence? We need to keep a running total. Here are the first 10 terms of the new sequence Term 1 1 Term 2 1+4=𝟓 Term 3 5+7=𝟏𝟐 Term 4 12+10=𝟐𝟐 Term 5 22+13=𝟑𝟓 Term 6 35+16=𝟓𝟏 Term 7 51+19=𝟕𝟎 Term 8 70+22=𝟗𝟐 Term 9 92+25=𝟏𝟏𝟕 Term 10 117+28=𝟏𝟒𝟓 Thus, the derived sequence is 𝟏, 𝟓, 𝟏𝟐, 𝟐𝟐, 𝟑𝟓, 𝟓𝟏, 𝟕𝟎, 𝟗𝟐, 𝟏𝟏𝟕, 𝟏𝟒𝟓