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The third term of an A.P is 4m - 2n. If the ninth term of the progression is 2m - 8n. Find the common difference in terms of m and n​

User Hamiltonia
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1 Answer

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Let
a_n denote the n-th term in the progression. So


a_n=a_(n-1)+d

for some constant difference between terms d.

Solve for
a_n explicitly:


a_4=a_3+d


a_5=a_4+d=a_3+2d


a_6=a_5+d=a_3+3d

and so on, up to


a_n=a_3+(n-3)d

We're told that the third term is
a_3=4m-2n, and the ninth term is
a_9=2m-8n, and according to the recursive rule above, we have


a_9=a_3+6d

Solve for d :


2m-8n=(4m-2n)+6d


-2m-6n=6d


d=-\frac{2m+6n}6=\boxed{-\frac{m+3n}3}

User Pedery
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