# Math Help - Arithmetic Sequence

1. ## Arithmetic Sequence

For a positive integer, consider the arithmetic sequence:

n, n+19, n+38, n+57,.......

The number 2013 may or may not belong to the sequence. What is the smallest positive integer n such that 2013 does belong to the sequence?

A) 4 B) 7 C) 11 D) 14 E) 18

2. ## Re: Arithmetic Sequence

Originally Posted by ConnieLam
For a positive integer, consider the arithmetic sequence:

n, n+19, n+38, n+57,.......

The number 2013 may or may not belong to the sequence. What is the smallest positive integer n such that 2013 does belong to the sequence?

A) 4 B) 7 C) 11 D) 14 E) 18

This sequence is $\{x: x=n+19k, k\in \mathbb{N}$

Divide 2013 by 19 to get

$2013 = 105 \times 19 +18$

Thus 18 will be the smallest $n$ such that 2013 is an element of the sequence.

3. ## Re: Arithmetic Sequence

use formula for AP

a(m)=a+(m-1)d
=n+(m-1)19
now here we have to find n
so here if m=106
(m-1)*19=1995
and a(m)=2013 so m=106
if m=107 n=-1 which is not possible
so n=18