Question

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

Answer 1

нєу тнєяє ιѕ αиѕωєя !!!!!

ι нσρє уσυ нєℓρ !!!


m times mth term= n times nth term

m am=n an

=> m{a+(m-1)d}= n{a+(n-1)d}

=>  m {a+(m-1)d} - n{a+(n-1)d}=0

=> am +m(m-1)d -an -n(n-1)d=0

=>am-an +m(m-1)d -n(n-1)d=0

=>a(m-n)+{m(m-1)-n(n-1)}d=0

=> a(m-n) +{m2-m-n2+n}d=0

=> a((m-n)+ {m2-n2-(m-n)} =0

=> a(m-n)+{(m-n)(m+n)-(m-n)}d =0

=> a(m-n)[(m-n){m+n-1}]d =0

=> (m-n) [a+(m+n-1)d]=0

=> a+(m+n-1)d=0

.`.  am+n =0

Hence, its (m+n)th term =0

hope this helpss.....

Answer 2

I hope this will help you