Question 129
If the sum and product of three consecutive terms of a geometric progression are 13 and 27 respectively, then the middle one of the three terms is
Solution
Let the 3 terms of the geometric progression be a/r , a , ar
Given, product of the terms = 27
$$\Rightarrow$$ $$\frac{a}{r}\times a\times ar=27$$
$$\Rightarrow$$ $$a^3=27$$
$$\Rightarrow$$ a = 3
Hence middle term = 3
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