How do you write the expression for the nth term of the sequence given #-2/3, 3/4, -4/5, 5/6, -6/7,...#?

1 Answer
Mar 6, 2017

We can write the expression for the #n^(th)# term of the sequence as #a_n=(-1)^n(n+1)/(n+2)#

Explanation:

Let us divide this in three parts.

First - Numerator goes like #{2,3,4,5,6,..}#. Here, we have arithmetic sequence with first term is #2# and common difference as #1# and hence #a_n=2+(n-1)xx1=n+1#

Second - Denominator goes like #{3,4,5,6,7,..}#. Here, we have arithmetic sequence with first term is #3# and common difference as #1# and hence #a_n=3+(n-1)xx1=n+2#

Third - The sign of every odd term is minus and every even term is plus and we can say that this is given by #(-1)^n#

Hence, we can write the expression for the #n^(th)# term of the sequence as

#a_n=(-1)^n(n+1)/(n+2)#