Question
Asked Nov 5, 2019
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Determine whether the sequence is increasing, decreasing, or not monotonic.
an=
4n23
increasing
decreasing
not monotonic
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Determine whether the sequence is increasing, decreasing, or not monotonic. an= 4n23 increasing decreasing not monotonic

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Expert Answer

Step 1
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For any sequence {a}, If a,a for every n(21), then {a} is increasing sequence. 2 i.e. aa <a <.-. If aa for every n(21), then {a} is decreasing sequence. i.e. а, > а, > а, >... If (ais either increasing or decreasing sequence, then it is called monotonic sequence; otherwise not.

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Step 2
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Let us check whether the sequence a 472 is increasing, decreasing or not +3 monotonic by finding the (n+1)th term of the sequence. Replace n by n+1 in the sequence a n+1 4(n+1)3 n+1 4(n2 +2n+1)+3 n1 4m2+8n 7 <a Therefore, a,>a for every n is decreasing sequence Thus the sequence a, : 4n 3

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Step 3
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We can verify that the sequence is decreasing by taking n=1 for both a, and a 2 > a 19 We will get a

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Calculus

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