How do you write the first five terms of the arithmetic sequence given #a_1=200, a_(k+1)=a_k-10# and find the common difference and write the nth term of the sequence as a function of n?

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Answer 1 · 2017-06-08T06:04:55

First ffive terms are #{200,190,180,170,160}#. Common difference is #10# and #n^(th)# term #a_n=210-10n#

As #a_(k+1)=a_k-10#, this means that

each succeeding term is #10# less than the previous term.

Hence #d# the common difference is given by #d=-10#

Now first term #a_1# is #200# and as #n^(th)# term is given by #a+(n-1)d=200+(n-1)xx(-10)=200-10n+10=210-10n#

and hence #a_2=a_1-10=200-10=190#

#a_3=a_2-10=190-10=180#

#a_4=a_3-10=180-10=170#

qnd #a_5=a_4-10=170-10=160#

Hence first ffive terms are #{200,190,180,170,160}#.