Sundar Pangeni's question at Yahoo Answers regarding arithmetic progressions

[MarkFL]

Here is the question:

Problem of arithmetic progression. Please help...?

The Mth term of an A.P. is N and the Nth term is M. The Rth term of it is...?
(a) M+N+R
(b)N+M-2R
(c)M+N+(R\2)
(d)M+N-R
(working note is required)

Here is a link to the question:

Problem of arithmetic progression. Please help...? - Yahoo! Answers

I have posted a link there to this topic so the OP can find my response.

 

[MarkFL]

Re: Sundar Pangeni's question at Yahoo! Answers regarding arithmethic progressions

Hello Sundar Pangeni,

The statement "The Mth term of an A.P. is N" tells us:

(1) \(\displaystyle a_M=a_1+(M-1)d=N\)

The statement "the Nth term is M" tells us:

(2) \(\displaystyle a_N=a_1+(N-1)d=M\)

Subtracting (2) from (1) we obtain:

\(\displaystyle (M-N)d=N-M\,\therefore\,d=-1\)

Substituting for $d$ into either (1) or (2) yields:

\(\displaystyle a_1=M+N-1\)

Hence:

\(\displaystyle A_R=a_1+(R-1)d=M+N-1+1-R=M+N-R\)

This is choice (d).

To Sundar Pangeni and any other guests viewing this topic, I invite and encourage you to post other arithmetic progression problems here in our http://www.mathhelpboards.com/f2/ forum.

Best Regards,

Mark.