if pth term of an ap is q and the q th term is p show that r th term is p+q-r

Asked by surain bhandari | 9th Aug, 2010, 07:17: PM

Expert Answer:

Dear Student,
 
Let the first term of the AP be A and common difference be D.
 
Now, from the given conditions,
 
A + (p-1)D = q and A + (q-1)D = p
 
Subtracting the two equations, we get
pD - D - qD + D = -(p - q)
=> (p - q)D = -(p - q)
=> D = -1
 
putting D = -1 in the first equation, we get
A = q + (p - 1) = p + q - 1
 
Therefore, the rth term of the AP is
A + (r - 1)D = p + q - 1 - r + 1 = p + q - 1
Hence, proved.
 
Regards Topperlearning.

Answered by  | 9th Aug, 2010, 09:04: PM

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