If the m times of the m th term of an ap is equal to the n times of the n th term, then find the (m+n)th term.

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- Jan 11th 2018, 03:27 AM #1

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- Jan 11th 2018, 04:11 AM #2

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## Re: Ap

"

**The**m of the mth term"? Do you mean just "m times the mth term"? The "mth term" of an arithmetic progression is a+ (m-1)d where "a" is the first term, and "d" is the common difference. "m times the mth term" would be m(a+ (m-1)d= (a+d)m- dm^2 and "n times the nth term" would be n(a+ (n-1)d)= (a+d)n- dn^2. If those are equal, (a+ d)m- dm^2= (a+ d)n- dn^2. (a+ d)m- (a+d)n= dm^2- dn^3. (a+ d)(m- n)= d(m^2- n^2)= d(m+ n)(m- n).

- Jan 11th 2018, 04:12 AM #3

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- Jan 12th 2018, 03:03 AM #4

- Jan 12th 2018, 05:22 PM #5

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