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If p times the p th term of an A.P. is equal to q times its q th term, show that the (p + q) th term of the A.P. is zero.

Posted by Md Sarfaraz 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let a be the first term and d be the common difference
p^th term = a +(p - 1)d = q(given)-----(1)
q^th term = a +(q - 1) d = p(given)-----(2)
subtracting (2) from (1)
(p-q)d=q-p
(p-q)d=-(p-q)
{tex}\therefore{/tex} d = -1
putting d=-1 in (i)
a - (p - 1) = q
{tex}\therefore{/tex} a=p+q-1
{tex}\therefore{/tex} (p + q)^th term = a + (p + q - 1)d
= (p + q - 1) - (p + q - 1) = 0

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CBSE > Class 10 > Mathematics