Question

plz slove the question ​

Answer 1

$tn= a + (n - 1)d \\ tm = a + (m - 1)d$
By given condition
$na + n(n - 1)d= am + m(m - 1)d \\ an + {n}^{2}d - nd = am + {m}^{2}d - md \\ am - an + {m}^{2}d - { {n}^{2}d + nd - md = }0 \\ a(m - n) + (m + n)(m - n)d - (m - n)d = 0$
divide equation by m-n
$a + (m + n)d - d= 0 \\ a + (m + n - 1)d = 0$
Hence proved