Number Theory
Integer Sequences
A general term of the sequence \[-8, -7, -9, -5, -13, 3, \cdots\] can be expressed as \(\displaystyle \frac{a-b^{n-1}}{3}\), where \(a\) and \(b\) are integers. What is the value of \(ab\)?
Which of the options represents the general term of the following sequence:
\[ 1, 8, 27, 64, 125 \ldots ? \]
Which of the options represents the general term of the following sequence:
\[ 2, 5, 28, 257, 3126, \ldots \]
Which of the options represents the general term of the following sequence:
\[ 4, 6, 8, 10, 12 \ldots ? \]
Which of the options represents the general term of the following sequence:
\[ 5, 9, 13, 17, 21 \ldots ? \]