Tag Archives: Arithmetic Sequence

Primes in Arithmetic Progression

Posted on January 9, 2015 by Sumant Sumant

Now n terms of arithmetic progression looks like . What this tells us that a must be prime (because is the first term),also and must be relative primes otherwise will not be prime. Also if the beginning term is we … Continue reading →

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Composite terms in arithmetic progression

Posted on January 8, 2015 by Sumant Sumant

Prove that there exists arbitrarily long arithmetic progressions whose terms are relatively prime in pairs and which consists entirely of composite numbers. Suppose we want to find n composite numbers which are pair wise prime. Recipe: Common difference is n! … Continue reading →

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Triangles with sides in Arithmetic Progression

Posted on January 7, 2015 by Sumant Sumant

Prove that if the lengths of the sides of a triangle are in arithmetic progression, then the line joining the centroid to the incenter is parallel to one of the sides. Let the sides be such that . We know … Continue reading →

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Summing all the digits from 1 to 9,999

Posted on May 24, 2014 by Sumant Sumant

If we look at the digits from 0000 to 9999. There are 10,000 different numbers. Since its a four digit number there digits. Since each digit appears equal number of times it means there are occurrence of each digit. So … Continue reading →

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