How do you write the first five terms of the sequence defined recursively #a_1=14, a_(k+1)=(-2)a_k#, then how do you write the nth term of the sequence as a function of n?

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Answer 1 · 2017-02-25T14:21:10

#a_n=14(-2)^((n-1))#

We are given #a_1=14# and as #a_(k+1)=(-2)a_k#, we have

#a_2=(-2)a_1=(-2)xx14=-28#

#a_3=(-2)a_2=(-2)xx(-28)=56#

#a_4=(-2)xxa_3=(-2)xx(56=-112# and

#a_5=(-2)xx(-112)=224#

It is apparent that it is geometric sequence with first term #a_1=14# and common ratio as #-2#. As such #n^(th)# term #a_n# is given by

#a_n=a_1xx(-2)^((n-1))=14(-2)^((n-1))#