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`1, sqrt 2, sqrt 3, 2` Find the general term.

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shayaan | Student, Undergraduate | Honors

Posted June 6, 2013 at 10:47 PM via web

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`1, sqrt 2, sqrt 3, 2`

Find the general term.

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mjripalda | High School Teacher | (Level 3) Educator

Posted June 7, 2013 at 1:37 AM (Answer #1)

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`1, sqrt2, sqrt3, 2`

To determine the general term, express the four terms as radicals.

Since,

`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.

`d=a_2-a_1=2-1=1`

`d=a_3-a_2=3-2=1`

`d=a_4-a_3=4-3=1`

Since they have common difference, apply the formula of arithmetic series in solving for nth term.

`a_n=a_1+(n-1)d`

Plug-in `a_1=1` and d=1.

`a_n=1+(n-1)1`

`a_n=1+n-1`

`a_n= n`

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` .

`a_n= sqrtn`

Hence, the general term of  `1, sqrt2, sqrt3, 2`  is   `a_n=sqrtn` .

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