Question

Determine whether the sequence converges or diverges. If it converges, give the limit: 72, 18. 9/2, 9/8, ...

Answer 1

Answer: The sequence converges. The limit it converges to is 0.

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The sequence is a geometric sequence with a = 72 and r = 1/4. Because 0 < r < 1, this means that the sequence gets smaller and smaller. The terms get closer to 0. They don't actually get there but the limiting value is 0.