# Arithmetic Sequence

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• Apr 18th 2014, 04:10 PM
ConnieLam
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

Please explain how you got the answer.
• Apr 18th 2014, 04:46 PM
romsek
Re: Arithmetic Sequence
Quote:

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

Please explain how you got the answer.

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.
• Apr 18th 2014, 09:03 PM
prasum
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