# Sundar Pangeni's question at Yahoo! Answers regarding arithmetic progressions

Staff member

#### MarkFL

Staff member
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 Pre-Algebra and Algebra forum.

Best Regards,

Mark.