Question

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

Answer 1

Answer:

refers to the attachment

Answer 2

Answer:

We have proved that, if m times the mth term is equal to n times the nth term of an A.P., (m+n)th term of A.P is equal to zero.

Step-by-step explanation:

We know that, according to the nth term of an AP we have,

nth term of AP = tₙ = a + (n − 1)d ------------- (1)

mth term of AP = tₘ = a + (m − 1)d ------------- (2)

According to the question, m times the mth term is equal to n times the nth term which can be written as,

mtₘ = ntₙ

From equation (1) and (2),

m[a + (m − 1)d] = n[a + (n − 1)d]

m[a + (m − 1)d] − n[a + (n − 1)d] = 0

a(m − n) + d[(m + n)(m − n) − (m − n)] = 0

(m − n)[a + d((m + n) − 1)] = 0

a + [(m + n) − 1]d = 0 ------------- (3)

But, a + [(m + n) − 1]d = tₘ ₊ ₙ

Thus, tₘ ₊ ₙ = 0 [From equation (3)].

Hence we have proved that, if m times the mth term is equal to n times the nth term of an A.P., (m+n)th term of A.P is equal to zero.

$thanks \: \\ brainlest \: please$