Question

If m times the mth term of an AP is equal to n times its nth term then show
that (m+n)th term of an AP is 0
only answer the question those who know​

Answer 1

Given:-

• m times the mth term of an AP is equal to n times its nth.

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To find:-

• Show that (m + n)th term of an AP is 0.

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Solution:-

Let,

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

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According to the question,

→ m x [a + (m - 1)d] = n x [a + (n - 1)d]

→ m(a + md - d) = n(a + nd - d)

→ am + m²d - md = an + n²d - nd

→ am + m²d - md - an - n²d + nd = 0

→ a(m - n) + d(m² - n²) - d(m - n) = 0

→ a(m - n) + d(m+n)(m-n) - d(m-n) = 0

→ (m - n){a + d(m + n) - d} = 0

→ a + (m + n - 1)d = 0

Hence Proved