Question

plz ans this fast n correctly​

Answer 1

Answer : 1

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

So,

• m'th term = a+(m-1)d
• n'th term = a+(n-1)d
• (m+n)th term = a+(m+n-1)d = x

Given :-

m x (m'th term) = n x (n'th term)

$\implies$ ma + dm(m-1) = na + dn(n-1)

$\implies$ ma-na+dm²-dm -dn² +dn = 0

$\implies$ a(m-n) +d(m²-n²)-d(m-n) = 0

$\implies$ a(m-n) +d(m-n) (m+n-1) =0

$\implies$ (m-n) [ a+d(m+n-1) ] = 0

$\implies$ [ a+d(m+n-1) ] = 0

Hence , x = 0

And therefore, ${249678}^{0}$ = 1