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if the sum of p term of an Ap is same as the sum of q term show that the sum of q and p is zero

Posted by Manvith R 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

S_p = S_q
{tex} \Rightarrow \frac{p}{2}\left[ {2a + (p - 1)d} \right] = \frac{q}{2}\left[ {2a + (q - 1)d} \right]{/tex}
{tex} \Rightarrow p\left[ {2a + pd - d} \right] = q\left[ {2a + qd - d} \right]{/tex}
{tex} \Rightarrow {/tex} 2ap + p²d - pd = 2aq + q²d - qd
{tex} \Rightarrow {/tex} 2a (p - q) + (p² - q²)d - (p - q)d = 0
{tex} \Rightarrow {/tex} 2a (p - q) + (p + q) (p - q)d - (p - q)d = 0
{tex} \Rightarrow {/tex} (p - q) [2a + (p + q - 1)d] = 0
{tex} \Rightarrow {/tex} S_p+q = 0

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CBSE > Class 10 > Mathematics