Question 2 - Relations among Number Sequences - Chapter 1 Class 6 - Patterns in Mathematics (Ganit Prakash)

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Question 2 By imagining a large version of your picture, or drawing it partially, as needed, can you see what will be the value of 1 + 2 + 3 + ... + 99 + 100 + 99 + ... + 3 + 2 + 1?From our sequence, we notice that 1 = 1 1 + 2 + 1 = 4 = 22 1 + 2 + 3 + 2 + 1 = 9 = 32 1 + 2 + 3 + 4 + 3 + 2 + 1 = 16 = 42 1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 = 25 = 52 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 36 = 62 So, it is the square of middle number Thus, 1 + 2 + 3 + ... + 99 + 100 + 99 + ... + 3 + 2 + 1 = 1002 = 10,000