# 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 3^{rd} 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 **0 ^{th}** 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 100^{th} 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 100^{th} term is 100(6) or 600. Now if we deduct 4 from it, we will get 596, which is choice D.