Question

If m times the mth term of an A.P. is eqaul to n times nth term then show that the
(m + n)th term of the A.P. is zero.​

Answer 1

Answer:

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11th

Maths

Sequences and Series

Arithmetic Progression

If m times the mth term of ...

MATHS

If m times the m

th

term of an A.P. is equal to n times n

th

term, show that the (m+n)

th

term of the A.P. is zero.

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ANSWER

Given,

nth term of AP =t

n

=a+(n−1)d

mth term of AP =t

m

=a+(m−1)d

⇒mt

m

=nt

n

m[a+(m−1)d]=n[a+(n−1)d]

m[a+(m−1)d]−n[a+(n−1)d]=0

a(m−n)+d[(m+n)(m−n)−(m−n)]=0

(m−n)[a+d((m+n)−1)]=0

a+[(m+n)−1]d=0

But t

m+n

=a+[(m+n)−1]d

∴t

m+n

=0

Step-by-step explanation:

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Answer 2

ANSWER

Given,

nth term of AP =tñ =a+(n−1)d

mth term of AP = tm =a+(m−1)d

⇒mtm = ntn

$m[a+(m−1)d]=n[a+(n−1)d]$

$m[a+(m−1)d]−n[a+(n−1)d]=0$

$a(m−n)+d[(m+n)(m−n)−(m−n)]=0$

$(m−n)[a+d((m+n)−1)]=0$

$But \: tm+n=a+[(m+n)−1]d$

$∴tm+n=0$

$proved$

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