Algebra
Geometric Progressions
Given that the first few terms of a geometric progression are \(6, 18, 54, 162 \ldots \), what is the common ratio of the geometric progression?
Given that the first, second, and third terms of a geometric progression are:
\[3, 9, 27 ... , \]
what is the fifth term?
In the geometric sequence \[\{ a_i \}_{i \geq 1} = \{ -7, 14, -28, \ldots, \} \] what is the value of \(n\) such that \(a_n = 224?\)
If the six numbers
\[7, k_1, k_2, k_3, k_4, \frac{7}{32}\]
form a geometric sequence in this order, what is \(k_2?\)
Given that the third, fourth, and fifth terms of a geometric progression are:
\[ \ldots, 45, 135, 405, \ldots, \]
what is the second term?