Question

If the sum of m terms of an AP is equal to the sum of either the next n terms or the next p terms, then prove that (m+n)(m1​−p1​)=(m+p)(m1​−n1​).

Answer 1

Answer:

If the sum of m terms of an AP is equal to the sum of either the next n terms or the next p terms, then prove that (m+n)(m1−p1)=(m+p)(m1−n1).

Answer 2

$\mathtt\red{answer}$

$\red{\frac{(m - n)x}{(m - p)x} = \frac{(m + n)nd}{(m + p)pd} }$

$\mathtt\red{ = (m - n)(m + p) p = (m - p)(m + n)n}$

$\underline\red{m + p ( \frac{1}{m} - \frac{1}{p} ) = (m + p)( \frac{1}{p} - \frac{1}{m} )}$

$\underline\red{= (m + n)( \frac{1}{m} - \frac{1}{p} ) = m + p( \frac{1}{m} - \frac{1}{n}) }$