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  • If A.M. between mth term and nth tem of A.P. is same as A.M. between pth term and qth term of A.P. Then which of the following is true for this A.P.&nbsp

If A.M. between mth term and nth tem of A.P. is same as A.M. between pth term and qth term of A.P. Then which of the following is true for this A.P. 

Option: 1

m+p=n+q


Option: 2

m-n=p-q


Option: 3

m+n=p+q


Option: 4

None of these


Answers (1)

best_answer

\\A.M._{1} =\frac{a+(m-1)d+a+(n-1)d}{2}\\ A.M._{1} =\frac{2a+(m+n-2)d}{2}\\ A.M._{2} =\frac{a+(p-1)d+a+(q-1)d}{2}\\ A.M._{2} =\frac{2a+(p+q-2)d}{2}\\ \\\text{Given } A.M. _{1}=A.M._{2}\\\\ \frac{2a+(m+n-2)d}{2} =\frac{2a+(p+q-2)d}{2}\\\\\Rightarrow m+n=p+q

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Sanket Gandhi

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