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The terms of an increasing sequence are getting larger and larger, so

un+1>un

whereas a decreasing sequence is getting smaller and smaller, so

un+1<un

If a sequence is increasing for all n, we say it is an increasing sequence (similar for decreasing).


  1. Show that the sequence

    un=n2+2n−10

    is an increasing sequence.

  2. Determine whether the sequence defined by

    un=n2−10n+4

    is an increasing sequence, a decreasing sequence, or neither.