Question 6 - Figure it out - Page 265, 266 - Chapter 10 Class 6 - The other side of Zero (Ganita Prakash)

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Question 6 (a) Complete the following sequences: (a) (–40), (–34), (–28), (–22), _____, ______, ______ The pattern is to add 6 to each number. So, we can write −22 + 6 = −16 −16 + 6 = −10 –10 + 6 = –4 The completed sequence is: (-40), (-34), (-28), (-22), -16, -10. -4,.. Question 6 (b) Complete the following sequences: (b) 3, 4, 2, 5, 1, 6, 0, 7, _____, _____, _____ This sequence is made of two separate patterns alternating Pattern 1 (starting at 3): 3, 2, 1, 0, ... (subtracting 1 each time) Pattern 2 (starting at 4): 4, 5, 6, 7, ... (adding 1 each time) Now, let’s find the next numbers Next number comes from Pattern 1: 0 − 1 = −1 Number after that comes from Pattern 2: 7 + 1 = 8 Number after comes from Pattern 1: –1 – 1 = –(1 + 1) = -2 The completed sequence is: 3, 4, 2, 5, 1, 6, 0, 7, -1, 8, –2,… Question 6 (c) Complete the following sequences: (c) _____, ______, 12, 6, 1, (–3), (–6), _____, ______, ______ The pattern here is in the difference between consecutive numbers. From 12 to 6, you subtract 6. From 6 to 1, you subtract 5. From 1 to -3, you subtract 4. From -3 to -6, you subtract 3. The amount you subtract decreases by 1 each time. Continuing the pattern: Subtract 2: −6−2 = −8 Subtract 1: −8 − 1 = −9 Subtract 0: −9 − 0 = −9 To find the first two numbers, we work backward (adding): Thus, we add numbers Since we subtracted 6, we must add 7: 12 + 7 = 19 Adding 8: 19 + 8 = 27 The completed sequence is: 27, 19, 12, 6, 1, (-3), (-6), -8, -9, -9