##
show

that th

times the mth term is equal to n times the nth term of an AP. Show that (m + n)th

term is zero (m + n)

Question

show

that th

times the mth term is equal to n times the nth term of an AP. Show that (m + n)th

term is zero (m + n).

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Mathematics
2 months
2021-08-06T07:47:24+00:00
2021-08-06T07:47:24+00:00 1 Answers
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## Answers ( )

Thge general nth 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