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# CBSE Class 10 Answered

if m times the m th term of an AP is equal to n times the n th term, show that the (m+n) th term of the AP is zero
Asked by prassanna.j | 13 Nov, 2023, 11:23: PM
Let a be the first term of Arithmetic Progression( AP )  and d be the common difference .

m-th term of AP is

m times of m-th term of AP is

.........................(1)

n-th term of AP is

m times of m-th term of AP is

.........................(2)

If  ( m tm ) = ( n tn ) then from eqn.(1) and (2) , we get

Dividing by (m-n) , we get

LHS of above expression is (m+n)th term of AP , i.e., t(m+n)

Hence (m+n)th term of AP is zero

Answered by Thiyagarajan K | 14 Nov, 2023, 11:07: AM

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