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).​

in progress 0
Emery 2 months 2021-08-06T07:47:24+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-08-06T07:48:46+00:00

    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

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