Mind Games on the Web -- Patterns

Vol 3, No 1 Presented by the Smart Science® system and Bill Graham as a free service for entertainment and education
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PATTERNS

by Bill Graham

brass weights Patterns are an integral part of math and science. Pattern recognition is an important tool used in solving many mathematical problems. Many scientific discoveries have been made as a result of noticing patterns in nature or in experimental data.

Look for patterns in the sequences below. Try to list the next five terms in each of the sequences. (Fair warning — they are not all mathematical sequences.)

bowling pins

1, 3, 6, 10, . . , (The difference between each pair of numbers keeps increasing by one. Also, this set of numbers are called triangular number since they form equilateral triangles. Ten, for example, would be the triangle formed by the pins in a bowling alley.)

2, 3, 5, 7, 11, 13, . . .

O, T, T, F, F, S, S, E, . . .

1, 4, 9, 16, . . .

1, 1, 2, 3, 5, 8, 13, . . .

1, 3, 4, 7, 8, 9, 13, 14, 15, 16, 21, . . .

2, 3, 5, 9, 17, . . .

1, 2, 6, __ , 120, 720, . . .

2, 10, 30, 68, 130, 222, . . .

12, 1, 1, 1, 2, 1, 3, . . .

Answer to Volume 3, Number 1