Question

In an arithmetic sequence ,if 'n'th term is m and 'm'th term is n .Prove that it's common difference is -1.​

Answer 1

Answer:

Step-by-step explanation:

d = common difference

Here, nth term,i.e,a(n)= a+(n-1)d =m [given]. ....(I)

and, mth term,i.e.,a(m)= a+(m-1)d =n [given]. ....(ii)

Subtracting (i) from (ii),we get-

(n-1)d-(m-1)d=m-n

or, d(n-1-m+1) = m-n

or, d(n-m) = -(n-m)

or, d = -1 ...

Hence, Proved...