# Thread: Find general term un

1. ## Find general term un

find the formula for Un, the genereal term of (2/3) , (4/5) , (6/7) , (8/9)

2. Originally Posted by peachgal
find the formula for Un, the genereal term of (2/3) , (4/5) , (6/7) , (8/9)
Dear peachgal,

Let me give you an idea, the denominator is always one greater than the numerator. (i.e: Numerator+1=Denominator) Therefore when you are writing the general term if the numerator is n then the denominator should be n+1. Now consider what the first term of the sequence is, that is when n=1 the numerator and denominator must be 2 and 3 respectively.

Hope you can continue.

3. Hello, peachgal!

Another view of the sequence . . .

Find the formula for $\displaystyle U_n$, the genereal term of: .$\displaystyle \frac{2}{3},\;\frac{4}{5},\;\frac{6}{7},\;\frac{8} {9},\;\hdots$

The numerators are even numbers:

. . $\displaystyle 2,\;4,\;6,\;8 \;\hdots\; 2n$

The denominators are one more than the numerators:

. . $\displaystyle 3,\;5,\;7,\;9\;\cdots\; 2n+1$

Got it?