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

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MarkFL

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Feb 24, 2012
13,775
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MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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.