Answer to Question #313764 in Analytic Geometry for Jane

Question #313764

p,p+7,p+14,.... is arithmetic sequence

Find n term and Find the smallest value of p for which 2021 is a term in the sequence.


1
Expert's answer
2022-03-19T02:35:35-0400

p,p+7,p+14,...p,p+7,p+14,...  is arithmetic sequence

a1=p,a2=p+7,a3=p+14,d=a2a1=7an=2021an=a1+d(n1)2021=p+7(n1)2021=p+7n77n=2028pn=2028p7nNn=2023+5p7n=289+5p75p=7k,kZp=57kk=0,p=5n=289a289=2021,p=5a_1=p, a_2=p+7, a_3=p+14, d=a_2-a_1=7\\ a_n=2021\\ a_n=a_1+d(n-1)\\ 2021=p+7(n-1)\\ 2021=p+7n-7\\ 7n=2028-p\\ n=\frac{2028-p}{7}\\ n\in N\\ n=\frac{2023+5-p}{7}\\ n=289+\frac{5-p}{7}\\ 5-p=7k, k\in Z\\ p=5-7k\\ k=0, p=5\\n=289\\ a_{289}=2021, p=5


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