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.
p,p+7,p+14,...p,p+7,p+14,...p,p+7,p+14,... is arithmetic sequence
a1=p,a2=p+7,a3=p+14,d=a2−a1=7an=2021an=a1+d(n−1)2021=p+7(n−1)2021=p+7n−77n=2028−pn=2028−p7n∈Nn=2023+5−p7n=289+5−p75−p=7k,k∈Zp=5−7kk=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=5a1=p,a2=p+7,a3=p+14,d=a2−a1=7an=2021an=a1+d(n−1)2021=p+7(n−1)2021=p+7n−77n=2028−pn=72028−pn∈Nn=72023+5−pn=289+75−p5−p=7k,k∈Zp=5−7kk=0,p=5n=289a289=2021,p=5
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