How do you write the nth term rule for the sequence 5/2,11/6,7/6,1/2,-1/6,...?

1 Answer
Aug 22, 2016

n^(th) term of the series is (19-4n)/6

Explanation:

In {5/2,11/6,7/6,1/2,-1/6...}, let us make denominator common. As GCD is 6, we can write the series as

{15/6,11/6,7/6,3/6,-1/6...}.

We observe that numerators form the series

{15,11,7,3,-1,...} which form an arithmetic series with first term a as 15 and common difference d between a term annd its preceding term is 12-15=-4. Hence, n^th term of this series is a+(n-1)d i.e. 15+(n-1)×(-4)=15-4n+4=19-4n

Hence n^(th) term of the series is (19-4n)/6