Question

If m times the mth term of an ap is equal to n times its nth term find the (m+n)th
term of the AP

Answer 1

Here is ur answer..........

Hope it helps!!☺☺

Answer 2

Answer: 0

Step-by-step explanation:

given that

m*mth term of an A.P = n* nth term of an A.P

let an A.P. with first term a and difference d

then

⇒m*[a+(m-1)*d]=n*[a+(n-1)*d]

⇒am+(m-1)*md=an+(n-1)*nd

⇒am-an=d[-(m-1)*m+(n-1)*n]

⇒a(m-n)=d[-m²+m+n²-n]

⇒a(m-n)=d[n²-m²+m-n]

⇒a(m-n)=d[(n-m)(n+m)+(m-n)]

⇒a(m-n)=d(m-n)[-(n+m)+1]

⇒a= -d[m+n-1] -------------- 1

now we have to find out the value (m+n)th term

we know

(m+n)th term of an A.P. = a+(m+n-1)*d

by putting the value of a from equation 1

⇒ -d[m+n-1] +(m+n-1)*d

=0

so (m+n)th term of this A.P. will be 0.