Question

The first S-number is 1. The second S-number is the sum of the first S-number and the second odd number. The third S-number is the sum of the second S-number and the third odd number. The fourth S-number is the sum of the third S-number and the fourth odd number, etc., …… Compute the first seven S-numbers. Make a note of any patterns you notice. Enter the first seven S-numbers as a comma-separated list:

Answer 1

• Sn = n^2 . . . . . . the pattern
• {1, 4, 9, 16, 25, 36, 49}

Explanation:

The consecutive differences between S-numbers are (by definition) consecutive odd numbers. This by itself indicates that S-numbers are defined by a quadratic formula. As it happens, ...

Sn = n^2

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S1 = 1 . . . . given

S2 = S1 + 3 = 4

S3 = S2 + 5 = 9

S4 = S3 + 7 = 16

S5 = S4 + 9 = 25

S6 = S5 +11 = 36

S7 = S6 +13 = 49

A list of the first 7 S-numbers is ...

{1, 4, 9, 16, 25, 36, 49}