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Sequences and Series

Geometric Progressions


Given that the first few terms of a geometric progression are 6,18,54,1626, 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...,3, 9, 27 ... ,

what is the fifth term?

In the geometric sequence {ai}i1={7,14,28,,}\{ a_i \}_{i \geq 1} = \{ -7, 14, -28, \ldots, \} what is the value of nn such that an=224?a_n = 224?

If the six numbers

7,k1,k2,k3,k4,7327, k_1, k_2, k_3, k_4, \frac{7}{32}

form a geometric sequence in this order, what is k2?k_2?

Given that the third, fourth, and fifth terms of a geometric progression are:

,45,135,405,, \ldots, 45, 135, 405, \ldots,

what is the second term?


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