Three consecutive terms of a Geometric Progression are − 6, p and − 32 . find the value of p.
you have a common ratio, so
p/-6 = -32/p
p^2 = 192
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To find the value of p, we need to identify the common ratio (r) of the geometric progression first.
Given the three consecutive terms of the geometric progression:
First term (a) = -6
Second term (p)
Third term (c) = -32
In a geometric progression, the ratio between any two consecutive terms is constant. So, we can set up the following equation:
p / -6 = -32 / p
To solve for p, we can cross-multiply:
p * p = -6 * -32
p^2 = 192
Taking the square root of both sides:
p = ± √192
Therefore, the value of p can be either √192 or -√192.