Question 24940: What are the definitons of recursive sequence and explicit sequence?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! IF NTH.TERM OF A SEQUENCE IS EXPRESSED EXPLICITLY AS A FUNCTION OF N THEN WE CALL IT AN EXPLICIT SEQUENCE.FOR EXAMPLE
TN=N*(N+1)....
FROM THIS WE CAN FIND ALLTERMS OF SEQUENCE BY JUST SUBSTITUTING DIFFERENT VALUES FOR N FROM 1,2,3....ETC.
T1=1*2
T2=2*3
T3=3*4...ETC.
ON THE OTHER HAND IF A SEQUENCE IS DEFINED BY RELATING THE N TH. TERM TO (N-1)TH. TERM BY A FORMULA AND ONE OF THE TERMS,USUALLY THE FIRST TERM,IS GIVEN EXPLICITLY,THEN WE CALL IT RECURSIVE SEQUENCE.
FOR EXAMPLE IF IT IS GIVEN THAT
TN=2*T(N-1)...AND T1=3,
THEN WE CAN ONLY FIND THE TERMS OF THE SEQUENCE RECURSIVELY STARTING FROM FIRST TERM OR ANY TERM NEEDED.HERE WE HAVE
T1=3...GIVEN
T2=2*T1=2*3
T3=2*T2=2*(2*3)
T4=2*T3=2*(2*(2*3))....ETC...
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