# Sequences I

In conventional math, an arithmetic sequence can be easily described by a simple algebraic expression when the common difference and the 0th term is known. This problem which was given during the 3rd International Vedic Mathematics Olympiad, Upper Primary group, illustrate how to determine the nth term of the sequence:

“A sequence starts, 2 8, 14, 20, 26, …. When it continues, what is the 100th number in the sequence?

A 582

B 588

C 594

D 596

E 602”

From the first five terms of the sequence, it is easy to see that the common difference, d, is 6. To determine the 0th term, we just need to subtract 6 from the first term, 2, to get – 4.

Thus the sequence can be described as 6n – 4 and the 100th term is 6(100) – 4 or 596. The intuitive solution is easier. After determining the common difference as 6, we just have to make the first term 6 by adding 4 to it. If we add 4 to each term of the sequence, we can see that all of them are multiples of 6. The 100th term is 100(6) or 600. Now if we deduct 4 from it, we will get 596, which is choice D.