How do you find the explicit formula for the following sequence 3,1, -1,-3, -5?

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Answer 1 · 2017-04-19T04:26:40

#n_(th)# term #a_n# is #5-2n#

Observe carefully, the difference of each term from its immediately preceding term is always constant, as

#1-3=-2#

#-1-1=-2#

#(-3)-(-1)=-3+1=-2# and

#-5-(-3)=-5+3=-2#

Hence,it is an arithmetic sequence with first term as #a_1=3# and common difference #d=-2#. Hence #n_(th)# term #a_n# is given by

#a_n=a_1+(n-1)×d#

= #3+(n-1)×(-2)#

= #3-2n+2#

= #5-2n#