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Let u , v , w be real numbers in geometric progression such that u > v > w . Suppose u ⁴⁰= v ^ n = w ⁶⁰ . Find the value of n .

Correct answer

48

Step-by-step solution

aligned & u=a & v=a r & w=a r^2 & a⁴⁰=(a r)^n= (a r^2 )⁶⁰ & a²⁰=r⁻¹²⁰ a=r⁻⁶ & r⁻²⁴⁰=r^ -5 n 5 n=240 & n= 240 5 =48 aligned

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