The sixth term in the sequence is -10
A recursive sequence is a sequence in which terms are defined using one or more previous terms which are given. If the nth term of an arithmetic sequence is known and the common difference d , you can find the (n+1)th term using the recursive formula an+1=an+d .
Given : f(1) = 5 and,
f(n) = f(n-1)-3 , for n = 2 ,3 , 4 , ...
Using the recursive formula to generate the terms, that is
f(2) = f(2-1)-3 = 5-3 = 2
f(3)= f(3-1)-3= f(2)-3= 2-3 = -1
f(4) = f(4-1)-3= -1-3= -4
f(5) = f(5-1)-3= -4-3= -7
f(6) = f(6-1)-3= -7-3= -10
Thus, sixth term in the sequence is -10.
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