√5/4,√3/2,√7/4. Find the formula for this sequence. √ this symbol means square root

Expert Answers

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I think that the root sign acts on entire fractions, i.e. we have the sequence

`sqrt(5/4),` `sqrt(3/2),` `sqrt(7/4).`

Let's express the second fraction as `6/4` and the sequence becomes

`sqrt(5/4), sqrt(6/4), sqrt(7/4).`

Now the rule is obvious: n-th term is `sqrt((n+4)/4)` if we start from `n=1.` This is the same as `sqrt(1+n/4).`

That said, there are infinitely many possible formulas for these three numbers, even among polynomial formulas.

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