The sequence {a_n} is defined by a_1= 1 and a_(n+1) = 1/2( a_n+ (4/a_n) ) for >=1. Assuming that {a_n} converges, find its limit.

Assuming convergence of the sequence, we have for some limit as . This also means . So in the above equation, we can substitute and solve for :

The limit can only be one of these values; otherwise, the sequence would be divergent. To decide which one is correct, we can observe that the sequence is strictly positive. So .

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175

the correct answer is x/3+10≥32

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