How do you write the first five terms of the sequence defined recursively #a_1=6, a_(k+1)=a_k+2#, then how do you write the nth term of the sequence as a function of n?

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Answer 1 · 2017-10-24T16:25:17

First five terms are #{6,8,10,12,14}# and #a_n=2n+4#

As #a_(k+1)=a_k+2# and#a_1=6#

#a_2=a_1+2=6+2=8#

#a_3=a_2+2=8+2=10#

#a_4=a_3+2=10+2=12#

and #a_5=a_4+2=12+2=14#

and hence first five terms are #{6,8,10,12,14}#

As #a_(k+1)=a_k+2#, each term is #2# more than previous term

it is an arithmetic sequence with first term as #a_1# and common difference #d# and hence #n^(th)# term is

#a_n=a_1+(n-1)d# and hence #n^(th)# term of the sequence is

#a_n=6+(n-1)xx2=6+2n-2=2n+4#