Number Theory

Integer Sequences

General Term Pattern Recognition

         

A general term of the sequence 8,7,9,5,13,3,-8, -7, -9, -5, -13, 3, \cdots can be expressed as abn13\displaystyle \frac{a-b^{n-1}}{3}, where aa and bb are integers. What is the value of abab?

Which of the options represents the general term of the following sequence:

1,8,27,64,125? 1, 8, 27, 64, 125 \ldots ?

Which of the options represents the general term of the following sequence:

2,5,28,257,3126, 2, 5, 28, 257, 3126, \ldots

Which of the options represents the general term of the following sequence:

4,6,8,10,12? 4, 6, 8, 10, 12 \ldots ?

Which of the options represents the general term of the following sequence:

5,9,13,17,21? 5, 9, 13, 17, 21 \ldots ?

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