Question

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किसी समांतर श्रेणी का m वा पद n और n वा पद m हो तो सिद्ध करें कि p वा पद m + n-p और (m + n) वाँ पद 0 होगा

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Answer 1

Hey Mate

your answer is--

Given, Tm = n

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

also, given

Tn = m

=> a + (n-1) d = m ....(2)

subtract equation (1) from (2) , we get

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

=> a+ dn - d - a - dm + d = m - n

=> d ( n - m ) = m - n

=> d = (m-n)/(n-m)

=> d = -(n-m)/(n-m)

=> d = -1 ...(3)

put this value in equation (1), we get

a + (m-1) -1 = n

=> a + (1-m) = n

=> a = n - (1-m) ...(4)

now, for p term

Tp = a + (p-1) d

= n - (1-m) + (p-1) -1

= n - 1 + m - p +1

= n +m - p

Now,

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

= n -1 + m -m-n+1

= -1 +1 = 0

【 Hope it helps you 】