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

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The problem presented involves finding the Rth term of an arithmetic progression (A.P.) where the Mth term is N and the Nth term is M. The solution reveals that the common difference (d) is -1, leading to the first term (a1) being M + N - 1. By substituting these values into the formula for the Rth term, the result is determined to be M + N - R, which corresponds to option (d). The discussion encourages further engagement by inviting others to share additional A.P. problems. This exchange highlights the collaborative nature of solving mathematical queries.
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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.
 
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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) $$a_M=a_1+(M-1)d=N$$

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

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

Subtracting (2) from (1) we obtain:

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

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

$$a_1=M+N-1$$

Hence:

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

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.
 
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