Writing the terms of a Recursively Defined Sequence Write down the first five terms

Question

Writing the terms of a Recursively Defined Sequence

Write down the first five terms of the following recursively defined sequence.

[latex]s_{1}=1,\ \ \ \ \ s_{n}=n s_{n-1}[/latex]

Accepted Answer

The first term is given as [latex]s_{1} = 1.[/latex] To get the second term, use [latex]n = 2[/latex] in the formula [latex]s_{n} = ns_{n-1}[/latex] to get [latex]{s}_{2}=2{s}_{1}=2\cdot 1=2.[/latex] To get the third term, use [latex]n = 3[/latex] in the formula to get [latex]s_{3}=3s_{2}=3\cdot 2=6.[/latex] To get a new term requires knowing the value of the preceding term. The first five terms are

[latex]\begin{array}{c}{{s_{1}=1}}\ {{s_{2}=2\cdot1=2}}\ {{s_{3}=3\cdot2=6}}\ {{s_{4}=4\cdot6=24}}\ {{s_{5}=5\cdot24=120}}\end{array}[/latex]

Do you recognize this sequence? [latex]s_{n} = n![/latex]

Question 11.11.1.5: Writing the terms of a Recursively Defined Sequence Write do......

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