A geometric progression has the same ratio between two consecutive terms. The seventh term of the geometric progression is 64/729.
What is a geometric sequence and how to find its nth terms?
Suppose the initial term of a geometric sequence is a
and the term by which we multiply the previous term to get the next term is r, Then the sequence would look like
[tex]a, ar, ar^2, ar^3, \cdots[/tex]
(till the terms to which it is defined)
Thus, the nth term of such sequence would be [tex]T_n = ar^{n-1}[/tex](you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).
Given the first term of the geometric progression is a₁=1. Also, the common ratio between the two terms is r= -(2/3). Therefore, the seventh term will be,
a₇ = a₁ × r⁽ⁿ⁻¹⁾
a₇ = 1 × -(2/3)⁶
a₇ = (64/729)
Hence, the seventh term of the geometric progression is 64/729.
Learn more about Geometric sequence:
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