Notes: `ln1, ln2, ln3, ln4, ln5` Determine whether the sequence is arithmetic. If so, find the common difference.

Thursday, January 30, 2014

$\displaystyle{\ln{{1}}},{\ln{{2}}},{\ln{{3}}},{\ln{{4}}},{\ln{{5}}}$ Determine whether the sequence is arithmetic. If so, find the common difference.

No, this sequence $\displaystyle{a}_{{n}}={\ln{{\left({n}\right)}}}$ is not an arithmetic one because the difference between the adjacent terms is not a constant. For example,

$\displaystyle{a}_{{2}}-{a}_{{1}}={\ln{{2}}}-{\ln{{1}}}={\ln{{2}}}$

but

$\displaystyle{a}_{{3}}-{a}_{{2}}={\ln{{3}}}-{\ln{{2}}}={\ln{{\left(\frac{{3}}{{2}}\right)}}}\ne{\ln{{\left({2}\right)}}}.$

No, this sequence $\displaystyle{a}_{{n}}={\ln{{\left({n}\right)}}}$ is not an arithmetic one because the difference between the adjacent terms is not a constant. For example,

$\displaystyle{a}_{{2}}-{a}_{{1}}={\ln{{2}}}-{\ln{{1}}}={\ln{{2}}}$

but

$\displaystyle{a}_{{3}}-{a}_{{2}}={\ln{{3}}}-{\ln{{2}}}={\ln{{\left(\frac{{3}}{{2}}\right)}}}\ne{\ln{{\left({2}\right)}}}.$

Notes

Thursday, January 30, 2014

$\displaystyle{\ln{{1}}},{\ln{{2}}},{\ln{{3}}},{\ln{{4}}},{\ln{{5}}}$ Determine whether the sequence is arithmetic. If so, find the common difference.

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Is Charlotte Bronte's Jane Eyre a feminist novel?

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Thursday, January 30, 2014

Determine whether the sequence is arithmetic. If so, find the common difference.

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Post a Comment

Is Charlotte Bronte&#39;s Jane Eyre a feminist novel?

$\displaystyle{\ln{{1}}},{\ln{{2}}},{\ln{{3}}},{\ln{{4}}},{\ln{{5}}}$ Determine whether the sequence is arithmetic. If so, find the common difference.

Is Charlotte Bronte's Jane Eyre a feminist novel?