How do you write the nth term rule for the sequence #4,1,-2,-5,-8,...#?

1 Answer
Aug 22, 2016

Answer:

#n^(th)# term in given sequence is #7-3n#.

Explanation:

This is an arithmetic sequence as the difference #d# between a term and its preceding term is always #-3# as #-3=1-4=-2-1=-5-(-2)=-8-(-5)#.

If first term is #a_1# and common difference in such arithmetic sequence is #d#,

#n^(th)# term is given by #a_1+(n-1)×d#. Hence #n^(th)# term in given series is

#4+(n-1)×(-3)#

= #4-3n+3#

= #7-3n#