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If the sum of m term of AP is the same as the sum of its n term then show that (m+n)th term is zero

Posted by Sushil Verma 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

ma_m = na_n
m[a + (m - 1)d] = n [a + (n - 1)d]
{tex} \Rightarrow {/tex} ma + m²d - md = na + n²d - nd
{tex} \Rightarrow {/tex} a(m - n) + (m² - n²)d - md + nd = 0
{tex} \Rightarrow {/tex} a(m - n) + (m - n) (m + n)d - (m - n)d = 0
{tex} \Rightarrow {/tex} (m - n) [a + (m + n - 1)d] = 0
{tex} \Rightarrow {/tex} a + (m + n - 1)d = 0
{tex} \Rightarrow {/tex} a_m+n = 0
Hence proved.

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CBSE > Class 10 > Mathematics