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`1, sqrt 2, sqrt 3, 2` Find the general term.
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High School Teacher
`1, sqrt2, sqrt3, 2`
To determine the general term, express the four terms as radicals.
`1=sqrt1` and `2 =sqrt4`
then the sequence becomes:
`sqrt1, sqrt2, sqrt3, sqrt4`
Next, consider the numbers inside the square root.
`a_1 = 1` `a_2= 2` `a_3=3` `a_4=4`
Then, determine if they have common difference.
Since they have common difference, apply the formula of arithmetic series in solving for nth term.
Plug-in `a_1=1` and d=1.
Since we only consider the number inside the square root, to determine the nth term of the given sequence, take the square root on `a_n` .
Hence, the general term of `1, sqrt2, sqrt3, 2` is `a_n=sqrtn` .
Posted by mjripalda on June 7, 2013 at 1:37 AM (Answer #1)
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