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If m times mth term of an A.P is equal to n times nth term of the A.P. Find its (m+n)th term

Posted by Moumita Bhowmik 6 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 3 months ago

Thge general n^th term of an AP is a + (n -1)d.

From the given conditions,

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

=> am + m²d - md = an + n²d - nd

=> a(m-n) + (m+n)(m-n)d - (m-n)d = 0

=> (m-n) ( a + (m+n-1)d ) = 0

Rejecting the non-trivial case of m=n, we assume that m and n are different.

=> ( a + (m + n - 1)d ) = 0

The LHS of this equation denotes the (m+n)^th term of the AP, which is Zero.

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