Mathematics

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21 Feb 2012 14:19:19 IST
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The m th term of an AP is n and the n th term is m. Find the sum of (m+n) terms.
CBSE Board , CBSE X , Mathematics

The m th term of an AP is n and the n th term is m. Find the sum of (m+n) terms.



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New kid on the Block

Joined: 20 Feb 2012
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26 Feb 2012 11:26:24 IST
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a +(m-1)d=n......................(1)

a +(n-1)d=m.........................(2)

substracting eq 1 from 2 we get:

d(m-n)=n-m

d=-(m-n)/m-n

d=-1.......................................(3)

putting the value of d in eq 1 we get 

a +(m-1)-1=n

a=n+m-1...........................(4)

Sm+n=m+n/2 *2(m+n-1)+(m+n-1)-1

Sm+n=(m+n)(m+n-1)/2 

 

and am+n=a + (m+n-1)-1

(puting the value of a from eq4 we get)

an=(m+n-1) - (m+n-1)

an=0 

 

 

edison's Avatar

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Joined: 19 Oct 2006
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26 Apr 2012 11:11:08 IST
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 Here mth term is Am = n

and nth term is An = m

Let first term = a

and common difference = d

Thus Am = n = a + (m -1) d   ...(1)

An = m = a + (n-1) d   ...(2)

Solving equations (1) and (2) simultaneously we obtain

d = -1

and a = n + m - 1

Thus sum of (m + n) terms is

S(m + n) = [(n + m) / 2] * [2a + ( n + m - 1)d] 

or S(m + n) =  [(n + m) / 2] * [2(n + m - 1) - ( n + m - 1)] 

or S(m + n) = (n + m) * (n + m - 1) / 2




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