Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • If m times mth term of AP is equal to n times of nth term of AP, then find the (m+n)th term of AP?

If m times mth term of AP is equal to n times of nth term of AP, then find the (m+n)th term of AP?

Answers (1)

Let 'a' be the first term and 'd' be the common difference of A.P.

The nth term of AP t_n = a + (n-1)d

Given: m times mth term of AP = n times nth term of AP

m[a + (m-1)d] =n[ a + (n-1)d] \\ am + m(m-1)d = an + n(n-1)d\\ a(m-n) + d(m^2-m) - (n^2-n)d = 0

a(m-n) + d(m^2- n^2)-d(m-n) = 0 \\ a(m-n) + d(m- n)(m+n)-d(m-n) = 0 \\ (m-n)[a+(m+n-1)d] = 0 \\ t_{m+n} = a+(m+n-1)d = 0

Hence, (m+n)th term of an AP is zero.

Posted by

Ravindra Pindel

View full answer

Similar Questions

Latest Question