Question

please answer me soon

first q terms (where p #q) then show that the sum of its first (p+q)
If the sum of the first p terms of an AP is the same as the sum of its
P
terms is zero.
Let a be the first term and d be the common difference of the
given AP. Then,
p
P
VO
Sp = Sq [2a + (p. – 1)d] = [2a + (9-1)d]
(p-9) (2a) = (q-p) (q + p - 1)d
► 2a = (1-p-9)d
Sum of the first (p+q) terms of the given AP
(p+q)
• {2a + (p+q-1)d}
... (1)​

Answer 1

pahle brain and answer karo FIR bataunga

Answer 2

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$let \: \: a \: \: be \: the \: first \: term \: and \: d \: be \: the \: common \: difference \: of \: the \: given \: ap \: \\ then \\ s _{p} = s _{q} \implies \frac{p}{2} (2a + (p - 1)d) = \frac{q}{2} (2a + (q - 1)d \\ \implies(p - q)(2a) = (q - p)(q + p - 1) \\ \implies2a = (1 - p - q)d \: \: \: \: \: \: \: .....(1) \\ sum \: of \: the \: first \: (p + q) \: terms \: of \: the \: given \: ap \\ = \frac{(p + q)}{2} (2a + (p + q - 1)d) \\ = \frac{(p + q)}{2} .(1 - p - q)d + (p + q - 1)d \: \: \: \: \: \: \: \: (using \: 1) \\ = 0$

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