SOLUTION: I can't seem to figure out the general term of this sequence. Could you help me out? The sequence is : 1, square root of 3, square root of 5, square root of 7, and square root of

Algebra ->  Sequences-and-series -> SOLUTION: I can't seem to figure out the general term of this sequence. Could you help me out? The sequence is : 1, square root of 3, square root of 5, square root of 7, and square root of      Log On


   

Question 91400This question is from textbook
: I can't seem to figure out the general term of this sequence. Could you help me out?
The sequence is : 1, square root of 3, square root of 5, square root of 7, and square root of 9.
I can tell that each time, you add two to the number, but I don't know how you would say that when using the (n)th term.
I would be very grateful if someone could help me. This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We basically have the sequence:

sqrt%281%29, sqrt%283%29, sqrt%28+5%29, sqrt%28+7%29, and sqrt%28+9%29...

since sqrt%281%29=1


So if we just look at the numbers inside the root and ignore the root for now we get the sequence

1,3,5,7,9....


Since the distance from term to term is d=2 and the starting term is a=1, we get the sequence

a%5Bn%5D=2n%2B1 where we start at n=0


Now just place that sequence in a square root like this

a%5Bn%5D=sqrt%282n%2B1%29