Question

.​if m times the mth term of an AP is equal to n times its nth term find its m+n th term

Answer 1

$\small \purple {\sf{quєѕtíσn !}}$

if m times the mth term of an AP is equal to n times its nth term find its m+n th term

$\small \blue {\sf{αnѕwєr :- }}$

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

Answer 2

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