Find an explicit formula for the following sequence, an which starts with a1=2/3. 2/3,3/4,4/5,5/6, ...

Step-by-step explanation:

a1=2/3

sequence is 2/3,3/4,4/5, ...

for numerator a1=2

d=3-2=1

numerator of nth term=a1 + (n-1) d=2 + (n-1) * 1=2+n-1=n+1

denominator = 1 more than numerator=n+1+1=n+2

so an = (n+1) / (n+2)

or for denominator a1=3, d=4-3=1

denominator of nth term=3 + (n-1) * 1=3+n-1=n+2

an = (n+1) / (n+2)