Please show how you get your formula or rule! I\'ve been stuck on this question

Question

Please show how you get your formula or rule! I've been stuck on this question all weekend. :)

For each of these lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list. Assuming that your formula or rule is correct, determine the next three terms of the sequence. 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, ... 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, ... 1, 0, 2, 0, 4, 0, 8, 0, 16, 0, ... 3, 6, 12, 24, 48, 96, 192, ... 15, 8, 1, -6, -13, -20, -27, ... 3, 5, 8, 12, 17, 23, 30, 38, 47, ...

Explanation / Answer

d)3,6,12,24,48,96,..

this is Geometric progression so

a=3 (first term of series)

r=6/3 =2 (common ratio)

so nth term of geometric series we can find by this formoula

T(n) =a * r(n-1)

T(n)=3*2(n-1)

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e)15,8,1,-6,....

this is Airthmatic progression so nth term of A.P we can find

here a=15 (first term of series),d =-7 (difference between two consecutive term of series)

so nth term T(n)=a+(n-1)*d

T(n)=15+(n-1)*(-7)

T(n)=22-7n ans.

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