Question

If n times n th term of an AP is equal to m times the m th term.Prove that (m + n) th
term is equal to zero.

Answer 1

Answer:

0

Step-by-step explanation:

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

In question,

= > m times of mth term = n times of nth term

= > m{a + (m - 1)d} = n{a + (n - 1)d}

= > am + md(m - 1) = an + nd(n - 1)

= > am - an = nd(n - 1) - md(m - 1)

= > a(m - n) = d(n² - n) - d(m² - m)

= > a(m - n) = d(n² - n - m² + m)

= > a(m - n) = d(n² - m² + m - n)

= > a(m - n) = d{(n - m)(n + m) + 1}

= > a(m - n) = d(m - n){ -(n + m) + 1)

= > a = - d(n + m - 1)

Thus, m + n th term:

= > a + (m + n - 1)d

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

= > 0