Barber Hall
10/18/2024 · Senior High School
4. Describe the following patterns in your own words, and then extend each pat sequence. \( \begin{array}{ll}\text { a) } 1 ; 3 ; 5 ; 7 ; 9 ; \ldots & \text { b) } 2 ; 1 ; 1 ; 1 ; \ldots \\ \text { c) } 6 ; 3 ; 0 ;-3 ;-6 ; \ldots & \text { d) } 1 ; 2 ; 4 ; 8 ; 16 ; \ldots \\ \text { e) } 4 ; 44 ; 484 ; 5324 ; \ldots & \text { f) } 1 ; 3 ; 6 ; 10 ; 15 ; \ldots\end{array} \)
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a) Odd numbers starting from 1, increasing by 2 each time. Extended sequence: 11; 13; 15; 17; 19; ...
b) Starts with 2, followed by a series of 1s. Extended sequence: 2; 1; 1; 1; 1; 1; 1; ...
c) Starts at 6, decreases by 3 each time. Extended sequence: -9; -12; -15; -18; ...
d) Powers of 2, doubling each time. Extended sequence: 32; 64; 128; 256; ...
e) Appends '4' to the previous number. Extended sequence: 53244; 532444; 5324444; ...
f) Triangular numbers, sum of first \(n\) natural numbers. Extended sequence: 21; 28; 36; 45; ...
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