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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Hello!

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.

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial